If A = bmatrix 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 bmatrix, then which of the following is the value of (adj A)^(-1) Option 1: bmatrix 1 & 2 & 3 \\ 2 & 1 & 2 \\ 3 & 4 & 1 bmatrix Option 2: bmatrix 1 & 1/2 & 1/3 \\ 1/2 & 1 & 1/2 \\ 1/3 & 1/4 & 1 bmatrix Option 3: 1/16bmatrix 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 bmatrix Option 4: -1/24bmatrix 1 & 2 & 3 \\ 2 & 1 & 2 \\ 3 & 4 & 1 bmatrix

Answer: 1/16bmatrix 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 bmatrix. Solution: Compute, A, = 1(1-8) - 2(2-12) + 3(4-3) = -7 + 20 + 3 = 16. Since A * adj(A) =, A, I, we have (adj A)^(-1) = A/(, A, ) = 1/16 A.

Algebra

Matrices & Determinants

Medium

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}$ , then which of the following is the value of $(\text{adj } A)^{-1}$

$\begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 2 \\ 3 & 4 & 1 \end{bmatrix}$

$\begin{bmatrix} 1 & 1/2 & 1/3 \\ 1/2 & 1 & 1/2 \\ 1/3 & 1/4 & 1 \end{bmatrix}$

$\frac{1}{16}\begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}$

$-\frac{1}{24}\begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 2 \\ 3 & 4 & 1 \end{bmatrix}$

✅ Correct Option: 3

Compute $|A| = 1(1-8) - 2(2-12) + 3(4-3) = -7 + 20 + 3 = 16$ . Since $A \cdot adj(A) = |A| I$ , we have $(adj\, A)^{-1} = \frac{A}{|A|} = \frac{1}{16} A$ .

2026: 12 May Shift 2

If $\begin{vmatrix}3 & x\\ x & 1\end{vmatrix}=\begin{vmatrix}3 & 2\\ 4 & 1\end{vmatrix}$ , then value of $x$ is/are

(A) $x=2$

(B) $x=-2$

(D) $x=-2\sqrt2$

Choose the correct answer from the options given below:

2026: 18 May Shift 1

For what values of $x$ and $y$ , are the following matrices equal?

$A=\begin{bmatrix}2x+1 & 3y\\ 0 & y^2-5y\end{bmatrix}$ , $B=\begin{bmatrix}x+3 & y^2+2\\ 0 & -6\end{bmatrix}$

2025: 19 May Shift 1

If A and B are square matrices of the same order 3, such that det (A) = 3 and AB = 3I, where I is an identity matrix of order 3. Then the value of det (B) is:

2026: 30 May Shift 1

The value of $\begin{vmatrix}1 & \log_ba\\\log_ab & 1\end{vmatrix}$ is:

2025: 30 May Shift 1

Let $A = [a_{ij}]_{n \times n}$ be a matrix, then match List-I with List-II

List-I	List-II
(A) $\vert A\vert = 0$	(I) $A$ is a symmetric matrix
(B) $\vert A\vert \neq 0$	(II) $A$ is a skew-symmetric matrix
(C) $A^T = A$	(III) $A$ is a singular matrix
(D) $A^T = -A$	(IV) $A$ is a non-singular matrix

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Match List-I with List-II

List-I	List-II
(Matrix)	(Determinant)
(A) $\begin{bmatrix} 1 & 7 \\ -3 & 5 \end{bmatrix}$	(I) 24
(B) $\begin{bmatrix} -2 & 5 \\ -3 & -3 \end{bmatrix}$	(II) 32
(C) $\begin{bmatrix} -12 & 8 \\ -16 & 8 \end{bmatrix}$	(III) 21
(D) $\begin{bmatrix} 15 & 9 \\ -21 & -11 \end{bmatrix}$	(IV) 26

Choose the correct answer from the options given below:

If A=[123214321]A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}A=​123​212​341​​, then which of the following is the value of (adj A)−1(\text{adj } A)^{-1}(adj A)−1

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 4 \\ 3 & 2 & 1 \end{bmatrix}$ , then which of the following is the value of $(\text{adj } A)^{-1}$