CUET UG Mathematics Booster Test 1 - Adjoint, Inverse Matrices and Applications of Determinants -

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CUET UG Mathematics Booster Test 1 - Adjoint, Inverse Matrices and Applications of Determinants

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Mathematics Booster Test 1 - Adjoint, Inverse Matrices and Applications of Determinants

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QUESTION 1 OF 20

Arrange the correct steps to form \(adj⁡(A)\)for \(A=[a_{ij}]\):
1. Find all minors \(M_{ij}\)
2. Apply signs to obtain cofactors \(A_{ij}=(-1)^{\left(i,\ j\right)}M_{ij}\)
3. Form the cofactor matrix \(\left[A_{ij}\right]\)
4. Transpose the cofactor matrix

Answer Review

1 Arrange the correct steps to form \(adj⁡(A)\)for \(A=[a_{ij}]\):
1. Find all minors \(M_{ij}\)
2. Apply signs to obtain cofactors \(A_{ij}=(-1)^{\left(i,\ j\right)}M_{ij}\)
3. Form the cofactor matrix \(\left[A_{ij}\right]\)
4. Transpose the cofactor matrix

A 1, 3, 2, 4

B 1, 2, 3, 4

C 2, 1, 3, 4

D 4, 3, 2, 1

💡 Short Explanation

Adjoint uses cofactors and transpose First compute minors Then apply signs and transpose

✅ Correct Answer Explanation

To construct \(adj⁡(A)\), first compute minors, then apply signs to obtain cofactors. Next form the cofactor matrix, and finally transpose it. Thus the correct order is: \(1\rightarrow 2\rightarrow 3\rightarrow 4\) Hence Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Cofactor matrix cannot be formed before applying sign factors.
Option C → Signs cannot be applied before calculating minors.
Option D → Transpose is the final step, not the first step.

🎯 Strategy

Used

Option Grouping

Application:

Arrange steps according to the standard adjoint-construction procedure.

Final Logic:

Adjoint is transpose of cofactor matrix obtained after minors and signs.

🧠 Memory Trick

"Minor → Sign → Cofactor → Transpose"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Adjoint of a Matrix

2 Which statements are correct?
I. Adjoint is defined only for square matrices
II. \(\left(i,\ j\right)\)element of \(adj⁡(A)\)is \(A_{ji}\)
III. It is required to compute \(A^{-1}\)when \(∣A∣\neq 0\)

A I and II

B II and III

C I and III

D I, II and III

💡 Short Explanation

Adjoint exists for square matrices Adjoint uses transpose of cofactors Inverse formula involves adjoint

✅ Correct Answer Explanation

All three statements are correct. Adjoint is defined only for square matrices. The \(\left(i,\ j\right)\)entry of \(adj⁡(A)\)equals the cofactor \(A_{ji}\)due to transposition. Also, \(A^{-1}=\frac{adj⁡(A)}{∣A∣}\) for non-singular matrices. Hence Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Ignores Statement III, which correctly relates adjoint to inverse computation.
Option B → Excludes Statement I, although adjoint is defined only for square matrices.
Option C → Omits Statement II, which correctly describes adjoint entries.

🎯 Strategy

Used

Option Grouping

Application:

Verify each statement independently using standard adjoint properties.

Final Logic:

All three statements satisfy the definition and inverse relation.

🧠 Memory Trick

"Adjoint = transpose of cofactors"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Adjoint and Inverse

3 Let
\(A=\left(\begin{pmatrix}1 & 2\\ 3 & 4\end{pmatrix}\right)\)
Find the sum of diagonal elements of \(adj⁡(A)\).
\(adj⁡(A)=\left(\begin{pmatrix}4 & -2\\ -3 & 1\end{pmatrix}\right)\)
Sum of diagonal \(=4+1=5\)

A 5

B 10

C −2

D −5

💡 Short Explanation

Adjoint diagonal entries are 4 and 1 Add principal diagonal terms Result equals 5

✅ Correct Answer Explanation

For: \(A=\left(\begin{pmatrix}1 & 2\\ 3 & 4\end{pmatrix}\right)\) Adjoint is: \(\left(\begin{pmatrix}4 & -2\\ -3 & 1\end{pmatrix}\right)\) Diagonal elements are 4 and 1. Their sum: \(4+1=5\) Hence Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Incorrect addition doubles the actual trace.
Option C → Negative value does not arise from adding diagonal entries.
Option D → Sign error occurs in diagonal summation.

🎯 Strategy

Used

Substitution

Application:

Use the given adjoint matrix and add its principal diagonal elements.

Final Logic:

Trace of the adjoint matrix equals 5.

🧠 Memory Trick

"Trace = sum of diagonal"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Adjoint Matrix

4 Identify the incorrect statement:

A Minor is obtained by deleting row and column

B Cofactor = \(\left(,\ 1)^{\left(i,\ j\right)}\right×\)minor

C \(adj⁡(A)\)is obtained by changing sign of determinant

D For 2×2, interchange \(a_{11}\)and \(a_{22}\)

💡 Short Explanation

Adjoint uses cofactors and transpose Determinant sign change is unrelated 2×2 adjoint swaps diagonal entries

✅ Correct Answer Explanation

Adjoint is formed by taking the transpose of the cofactor matrix, not by changing the sign of the determinant. Thus Option C is incorrect. Options A and B correctly define minors and cofactors, while Option D describes the standard 2×2 adjoint construction rule.

❓ Why Other Options Are Incorrect

Option A → Correct definition of a minor.
Option B → Correct cofactor formula using checkerboard sign pattern.
Option D → Correct rule for forming adjoint of a 2×2 matrix.

🎯 Strategy

Used

Elimination

Application:

Compare each statement with the formal definition of adjoint.

Final Logic:

Adjoint depends on cofactors and transpose, not determinant sign change.

🧠 Memory Trick

"Adjoint = transpose of cofactors"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Construction of Adjoint

5 If a matrix is singular, its determinant is:

A Negative

B Zero

C Positive

D Undefined

💡 Short Explanation

Singular matrices are non-invertible Zero determinant defines singularity Inverse does not exist

✅ Correct Answer Explanation

A matrix is singular if: \(∣A∣=0\) Such matrices are non-invertible because division by zero determinant is impossible in inverse formulas. Hence Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Negative determinants may still correspond to invertible matrices.
Option C → Positive determinants also allow inverses.
Option D → Determinants are always defined for square matrices.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Recall the standard algebraic definition of singular matrices.

Final Logic:

Singularity is directly linked to zero determinant.

🧠 Memory Trick

"Singular ⇒ determinant zero"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Singular Matrix

6 If \(∣A∣=0\), the probability that \(A\) is non-invertible is:

A 0

B 1

C 0.5

D 0.25

💡 Short Explanation

Zero determinant implies singularity Singular matrices are never invertible Probability becomes certain

✅ Correct Answer Explanation

If: \(∣A∣=0\) then the matrix is singular. Singular matrices do not possess inverses. Therefore the probability that \(A\) is non-invertible equals 1. Hence Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Invertibility is impossible when determinant is zero.
Option C → No uncertainty exists; the condition guarantees singularity.
Option D → Non-invertibility is certain, not partial.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Use the determinant criterion for invertibility directly.

Final Logic:

Zero determinant guarantees non-invertibility.

🧠 Memory Trick

"Determinant zero → inverse impossible"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Invertibility Condition

7 If determinant \(=\pm 8\neq 0\), the matrix is:

A Null

B Singular

C Non-singular

D Identity

💡 Short Explanation

Nonzero determinant implies invertibility Singular matrices require zero determinant Matrix becomes non-singular

✅ Correct Answer Explanation

Since: \(∣A∣=\pm 8\neq 0\) the determinant is nonzero. Therefore the matrix is invertible and hence non-singular. Thus Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Null matrices have determinant zero.
Option B → Singular matrices require determinant equal to zero.
Option D → Identity matrices specifically have determinant 1.

🎯 Strategy

Used

Elimination

Application:

Apply the determinant criterion for singularity and invertibility.

Final Logic:

Any nonzero determinant implies non-singular matrix.

🧠 Memory Trick

"Nonzero determinant ⇒ inverse exists"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Non-Singular Matrices

8 A matrix is invertible if it is:

A Zero matrix

B Singular

C Symmetric

D Non-singular

💡 Short Explanation

Invertibility requires nonzero determinant Non-singular matrices satisfy condition Singular matrices lack inverses

✅ Correct Answer Explanation

A matrix is invertible when: \(∣A∣\neq 0\) Such matrices are called non-singular. Therefore Option D is correct. Symmetry alone does not guarantee invertibility.

❓ Why Other Options Are Incorrect

Option A → Zero matrix always has determinant zero.
Option B → Singular matrices cannot have inverses.
Option C → Symmetric matrices may still be singular.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Use the standard equivalence between invertibility and non-singularity.

Final Logic:

Invertibility requires a nonzero determinant.

🧠 Memory Trick

"Non-singular means invertible"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Invertible Matrices

📄 Passage

Matrix equation: \(AX=B\)

Inverse formula:
\(A^{-1}=\frac{adj⁡(A)}{∣A∣}\)
If \(∣A∣=0\), compute \((adj⁡A)B\) to check consistency.
Which formula gives inverse?

A \(A^{-1}=\frac{\operatorname{adj}\,A}{∣A∣}\)

B \(A^{-1}=\frac{∣A∣}{\operatorname{adj}\,A}\)

C \(A^{-1}=∣adj⁡A∣\)

D \(A^{-1}=\frac{A}{∣A∣}\)

💡 Short Explanation

Inverse uses adjoint and determinant Determinant must be nonzero Standard inverse formula

✅ Correct Answer Explanation

For a non-singular matrix: \(A^{-1}=\frac{adj⁡(A)}{∣A∣}\) This is the standard inverse formula. Hence Option A is correct. Other expressions misuse determinants or adjoints algebraically.

❓ Why Other Options Are Incorrect

Option B → Determinant cannot be divided by a matrix meaningfully here.
Option C → Determinant of adjoint is not the inverse matrix.
Option D → Dividing matrix entries directly by determinant does not produce inverse.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Use the inverse formula stated directly in the passage.

Final Logic:

Inverse equals adjoint divided by determinant.

🧠 Memory Trick

"Inverse = adjoint over determinant"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Inverse Using Adjoint

📄 Passage

Matrix equation: \(AX=B\)

Inverse formula:
\(A^{-1}=\frac{adj⁡(A)}{∣A∣}\)
If \(∣A∣=0\), compute \((adj⁡A)B\) to check consistency.
If \(A\) is singular, compute:

A \(adj⁡A+B\)

B \(A^{-1}B\)

C \((adj⁡A)B\)

D \(∣A∣B\)

💡 Short Explanation

Singular matrices lack inverses Consistency uses adjoint multiplication Passage directly states required computation

✅ Correct Answer Explanation

When: \(∣A∣=0\) the inverse does not exist. In such cases, consistency of the system is checked using: \((adj⁡A)B\) as stated in the passage. Hence Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Simple addition has no consistency-checking role.
Option B → Inverse cannot exist for singular matrices.
Option D → Multiplying by determinant does not test consistency.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Use the exact instruction given in the passage for singular matrices.

Final Logic:

Singular systems are checked using \((adj⁡A)B\).

🧠 Memory Trick

"Singular? Use adjoint-times-B"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Consistency of Matrix Equations

11 Given dataset: 2,3,5,X.
The moving average of period 2 for the last two values is:
\(\frac{5+X}{2}\)
Also,
\(∣AB∣=∣A∣∣B∣=3\times 2=6\)
So,
\(\frac{5+X}{2}=6\Rightarrow 5+X=12\Rightarrow X=7\)

A 5

B 6

C 8

D 7

💡 Short Explanation

Use moving-average formula Equate with determinant product value Solve resulting linear equation

✅ Correct Answer Explanation

The moving average of the last two values is: \(\frac{5+X}{2}\) Given: \(∣AB∣=∣A∣∣B∣=3\times 2=6\) Equating: \(\frac{5+X}{2}=65+X=12X=7\) Thus Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Substitution gives moving average \(=5\), not 6.
Option B → Produces moving average \(5.5\), not the required value.
Option C → Gives moving average \(6.5\), exceeding the condition.

🎯 Strategy

Used

Substitution

Application:

Substitute determinant-product value into the moving-average equation.

Final Logic:

Solving the equation yields \(X=7\).

🧠 Memory Trick

"Average equation → isolate \(X\)"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Product of Determinants

12 Match expressions with meanings:

List I	List II
1. \(AB=I\)	a. Invertibility condition
2. \(∣A∣\neq 0\)	b. \(B\) is inverse of \(A\)
3. \(A(adj⁡A)=∣A∣I\)	c. Fundamental adjoint theorem

A 1–a, 2–b, 3–c

B 1–b, 2–a, 3–c

C 1–c, 2–b, 3–a

D 1–a, 2–c, 3–b

💡 Short Explanation

Identity product indicates inverse Nonzero determinant ensures invertibility Adjoint theorem connects determinant and adjoint

✅ Correct Answer Explanation

If: \(AB=I\) then \(B\) is inverse of \(A\). Also, \(∣A∣\neq 0\) is the condition for invertibility. Finally, \(A(adj⁡A)=∣A∣I\) is the fundamental adjoint theorem. Hence matching is: \(1-b, 2-a, 3-c\) Therefore Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Incorrectly swaps inverse relation and invertibility condition.
Option C → Fundamental adjoint theorem is mismatched.
Option D → Identity product does not itself represent invertibility condition.

🎯 Strategy

Used

Option Grouping

Application:

Match each matrix expression with its standard algebraic interpretation.

Final Logic:

Each expression corresponds uniquely to a known theorem or condition.

🧠 Memory Trick

"AB=I means inverse"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Fundamental Theorems

13 Evaluate:
\(\int_{0}^{1}\,2x dx=[x^{2}]_{0}^{1}=1\)

A 1

B 2

C 0

D 0.5

💡 Short Explanation

Integrate \(2x\) to get \(x^{2}\) Apply limits carefully Final value equals 1

✅ Correct Answer Explanation

Integrating: \(\int 2x dx=x^{2}\) Applying limits: \(\left[x^{2}]_{0}^{1}=1^{2}-0^{2}=1\right.\) Thus Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Incorrectly doubles the evaluated result.
Option C → Ignores upper-limit contribution.
Option D → Represents incorrect integration or averaging.

🎯 Strategy

Used

Substitution

Application:

Apply definite integration formula using upper and lower limits.

Final Logic:

\(1^{2}-0^{2}=1\).

🧠 Memory Trick

"Integral of \(2x\)→ \(x^{2}\)"

📚 Class XII – NCERT Mathematics Part 2 – Chapter: Integrals – Topic: Definite Integrals

14 Assertion (A): \(X=A^{-1}B\) gives the unique solution when \(A\) is non-singular.
Reason (R): Premultiplying \(AX=B\) by \(A^{-1}\)gives \(A^{-1}A=I\).

A Both false

B A true, R false

C Both true, R explains A

D A false, R true

💡 Short Explanation

Non-singular matrices have inverses Premultiplication produces identity matrix Unique solution follows immediately

✅ Correct Answer Explanation

For a non-singular matrix: \(A^{-1} exists\) From: \(AX=B\) Premultiplying by \(A^{-1}\): \(A^{-1}AX=A^{-1}BIX=A^{-1}BX=A^{-1}B\) Thus both statements are true and the Reason correctly explains the Assertion.

❓ Why Other Options Are Incorrect

Option A → Both statements are standard matrix-equation results.
Option B → Reason is true because inverse multiplication gives identity matrix.
Option D → Assertion is correct for non-singular matrices.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Relate inverse multiplication directly to matrix-equation solving.

Final Logic:

Inverse existence guarantees unique solution.

🧠 Memory Trick

"Multiply by inverse → isolate \(X\)"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Solution of Matrix Equations

15 Two linearly independent vectors in a plane correspond to:

A Zero solutions

B Two solutions

C Infinite solutions

D Exactly one solution

💡 Short Explanation

Linear independence implies non-singularity Unique representation exists System has exactly one solution

✅ Correct Answer Explanation

Two linearly independent vectors form a basis in the plane. The corresponding coefficient matrix becomes non-singular, ensuring a unique solution for the associated system. Hence Option D is correct.

❓ Why Other Options Are Incorrect

Option A → Linear independence does not eliminate all solutions.
Option B → Systems generally have one unique solution, not exactly two.
Option C → Infinite solutions occur only under dependence conditions.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Use the relationship between linear independence and invertibility.

Final Logic:

Independent vectors guarantee a unique solution.

🧠 Memory Trick

"Independent ⇒ unique"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Consistent Systems

16 Which conditions imply inconsistency?
I. \(∣A∣=0\)
II. \((adj⁡A)B\neq 0\)
III. Infinite solutions

A I and II

B II and III

C I and III

D I, II and III

💡 Short Explanation

Singular systems may become inconsistent Adjoint condition tests compatibility Infinite solutions imply consistency

✅ Correct Answer Explanation

If: \(∣A∣=0\) the system is singular. Further, if: \((adj⁡A)B\neq 0\) the system becomes inconsistent. Infinite solutions indicate consistency, not inconsistency. Hence Statements I and II are correct, making Option A correct.

❓ Why Other Options Are Incorrect

Option B → Infinite solutions correspond to consistent dependent systems.
Option C → Infinite solutions do not imply inconsistency.
Option D → Statement III contradicts inconsistency conditions.

🎯 Strategy

Used

Elimination

Application:

Separate inconsistent conditions from infinitely consistent cases.

Final Logic:

Only Statements I and II imply inconsistency.

🧠 Memory Trick

"Singular + incompatible ⇒ inconsistent"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Consistency of Equations

17 For a unique solution, \(∣A∣\)must be:

A 0

B \(\neq 0\)

C 1

D Negative

💡 Short Explanation

Unique solution requires inverse Inverse exists for nonzero determinant Non-singular matrices guarantee uniqueness

✅ Correct Answer Explanation

A unique solution exists only when: \(∣A∣\neq 0\) Then \(A\) is non-singular and invertible, allowing: \(X=A^{-1}B\) Hence Option B is correct.

❓ Why Other Options Are Incorrect

Option A → Zero determinant produces singular systems.
Option C → Determinant need not equal exactly 1.
Option D → Determinant may be positive or negative as long as nonzero.

🎯 Strategy

Used

Elimination

Application:

Use the determinant criterion for invertibility and uniqueness.

Final Logic:

Nonzero determinant guarantees unique solution.

🧠 Memory Trick

"Unique ⇒ determinant nonzero"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Unique Solution Criterion

18 \(A=\left(\begin{pmatrix}1 & 2\\ 2 & 4\end{pmatrix}\right)∣A∣=1⋅4-2⋅2=4-4=0\)

A 0

B −2

C 2

D 8

💡 Short Explanation

Use \(ad-bc\) formula Rows are proportional Determinant becomes zero

✅ Correct Answer Explanation

For: \(A=\left(\begin{pmatrix}1 & 2\\ 2 & 4\end{pmatrix}\right)\) Determinant: \(∣A∣=1(4)-2(2)=4-4=0\) Hence Option A is correct. The matrix is singular because its rows are proportional.

❓ Why Other Options Are Incorrect

Option B → Incorrect subtraction during determinant evaluation.
Option C → Ignores cancellation of equal products.
Option D → Represents multiplication instead of determinant subtraction.

🎯 Strategy

Used

Substitution

Application:

Apply the 2×2 determinant formula directly.

Final Logic:

Equal products cancel, giving determinant zero.

🧠 Memory Trick

"Proportional rows ⇒ determinant zero"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Singular Matrices

19 Arrange the following steps involved in solving a system of linear equations using the inverse matrix method in the correct sequence.
1. Define the variables.
2. Form the equations from the given problem.
3. Write the system in matrix form \(AX=B\).
4. Solve using \(X=A^{-1}B\).

A 1, 2, 4, 3

B 2, 1, 3, 4

C 1, 2, 3, 4

D 3, 1, 2, 4

💡 Short Explanation

Define the unknown variables first. Translate the information into linear equations. Express the equations in matrix form and apply the inverse method.

✅ Correct Answer Explanation

The inverse matrix method follows a systematic procedure. Step 1: Define the unknown variables. Example: Let x = first unknown y = second unknown Step 2: Form the required linear equations from the given information. Example: 2x + 3y = 8 x − y = 1 Step 3: Express the equations in matrix form. AX = B where A = Coefficient matrix X = Variable matrix B = Constant matrix That is, A = | 2 3 | | 1 -1 | X = | x | | y | B = | 8 | | 1 | Step 4: Find the inverse of A (if it exists) and compute X = A⁻¹B This gives the values of the unknown variables. Therefore, the correct sequence is 1 → 2 → 3 → 4 Hence, Option C is correct.

❓ Why Other Options Are Incorrect

Option A → Incorrect because the inverse method cannot be applied before writing the matrix equation.
Option B → Incorrect because variables must be defined before forming equations.
Option D → Incorrect because the matrix equation cannot be written before defining variables and forming the equations.

🎯 Strategy

Used: Contextual/Tonal Matching

Application:

Arrange the steps according to the standard NCERT procedure for solving simultaneous linear equations using the inverse matrix method.

Final Logic:

Define variables → Form equations → Write matrix equation → Apply the inverse matrix method.

🧠 Memory Trick

"Define → Form → Matrix → Inverse"

📚 Class XII – NCERT Mathematics Part I – Chapter: Matrices – Topic: Solution of System of Linear Equations Using the Inverse of a Matrix

20 Identify incorrect statement:

A Uses matrix inversion

B \(A\) is coefficient matrix

C Works for consistent systems

D Uses addition of determinants to find \(X\)

💡 Short Explanation

Matrix method uses inverses Coefficient matrix forms system Determinant addition is unrelated

✅ Correct Answer Explanation

The matrix method solves: \(AX=B\) using: \(X=A^{-1}B\) It relies on inverses and coefficient matrices, not addition of determinants. Therefore Option D is incorrect. Options A, B, and C correctly describe the matrix method.

❓ Why Other Options Are Incorrect

Option A → Matrix inversion is a standard solving technique.
Option B → \(A\) indeed represents the coefficient matrix.
Option C → Matrix inversion works only for consistent non-singular systems.

🎯 Strategy

Used

Elimination

Application:

Compare each statement with the standard inverse-matrix method.

Final Logic:

Determinants are not added to compute solution vectors.

🧠 Memory Trick

"Inverse solves, determinants don't add"

📚 Class XII – NCERT Mathematics Part 1 – Chapter: Determinants – Topic: Matrix Equation Method

CUET UG Mathematics Booster Test 1 - Adjoint, Inverse Matrices and Applications of Determinants

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