Match List I with List II: Given that A and B are invertible matrices of size 3 x 3, List I, List II, A. AB, I. 1/( A ), B. Adj A, II. A B, C. A^(-1), III. B^(-1) * A^(-1), D. (AB)^(-1), IV. A ^2, Choose the correct answer from the options given below: Option 1: A-II, B-I, C-III, D-IV Option 2: A-IV, B-II, C-I, D-III Option 3: A-III, B-IV, C-II, D-I Option 4: A-II, B-IV, C-I, D-III

Answer: A-II, B-IV, C-I, D-III. Solution: A:, AB, =, A, B, matches II. B:, adj\ A, =, A, ^(n-1) =, A, ^2 for n=3 matches IV. C:, A^(-1), = 1/(, A, ) matches I. D: (AB)^(-1) = B^(-1)A^(-1) matches III. So A-II, B-IV, C-I, D-III.

Algebra

Matrices & Determinants

Easy

Match List I with List II: Given that A and B are invertible matrices of size $3 \times 3$

List I List II
A. $\lvert AB \rvert$ I. $\frac{1}{\lvert A \rvert}$
B. $\lvert \operatorname{Adj} A \rvert$ II. $\lvert A \rvert \lvert B \rvert$
C. $\lvert A^{-1} \rvert$ III. $B^{-1} \cdot A^{-1}$
D. $(AB)^{-1}$ IV. $\lvert A \rvert^2$

Choose the correct answer from the options given below:

List I	List II
A. $\lvert AB \rvert$	I. $\frac{1}{\lvert A \rvert}$
B. $\lvert \operatorname{Adj} A \rvert$	II. $\lvert A \rvert \lvert B \rvert$
C. $\lvert A^{-1} \rvert$	III. $B^{-1} \cdot A^{-1}$
D. $(AB)^{-1}$	IV. $\lvert A \rvert^2$

A-II, B-I, C-III, D-IV

A-IV, B-II, C-I, D-III

A-III, B-IV, C-II, D-I

A-II, B-IV, C-I, D-III

✅ Correct Option: 4

A: $|AB| = |A||B|$ matches II.

B: $|adj\ A| = |A|^{n-1} = |A|^2$ for $n=3$ matches IV.

C: $|A^{-1}| = \frac{1}{|A|}$ matches I.

D: $(AB)^{-1} = B^{-1}A^{-1}$ matches III.

So A-II, B-IV, C-I, D-III.

2025: 3 June Shift 1

If $A = \begin{bmatrix} 1 & 2 \\ 4 & 5 \end{bmatrix}$ , then

Match List-I with List-II

List-I	List-II
(A) det (A)	(I) $-\frac{1}{3}$
(B) det $(A^{-1})$	(II) $-12$
(C) det (2A)	(III) $-3$
(D) det $(3A^T)$	(IV) $-27$

Choose the correct answer from the options given below:

2026: 12 May Shift 2

The matrix which is both symmetric and skew-symmetric, is a:

2025: 14 May Shift 2

If A is a square matrix of order 3 such that $|A| = 3$ , then $|adj(adj A)|$ is equal to:

2022: 17 Aug Shift 2

If $x = \begin{vmatrix}1 & 2 & 3 \\ 2 & 3 & 1 \\ 3 & 1 & 2\end{vmatrix}$ then value of $9-2x$ is :

2026: 29 May Shift 1

Let $A=\begin{bmatrix}2 & 2 & 2 \\ 0 & 2 & 2 \\ 0 & 0 & 2\end{bmatrix}$ , then $A^6$ is equal to:

2025: 22 May Shift 1

Let $A = \begin{bmatrix} 152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0 \end{bmatrix}$ . If $A_{ij}$ denotes the co-factor of an element $a_{ij}$ of the matrix A, then the value of $a_{11}A_{21} + a_{12}A_{22} + a_{13}A_{23}$ is equal to

Solution

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