If A is a matrix of order 3 x 3 such that, A, = 4 and, k * adj A, = 32, A, k R; then the value of k is: Option 1: 1 Option 2: 2 Option 3: 4 Option 4: 8

Answer: 2. Solution: adj A, =, A, ^2 = 16 for a 3x3 matrix. So, k adj A, = k^3(16) = 32(4) = 128, giving k^3 = 8 and k = 2.

Algebra

Matrices & Determinants

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If A is a matrix of order $3 \times 3$ such that $|A| = 4$ and $|k \cdot adj\, A| = 32|A|, k \in \mathbb{R}$ ; then the value of k is:

✅ Correct Option: 2

$|adj\,A| = |A|^2 = 16$ for a $3\times3$ matrix.

So $|k\,adj\,A| = k^3(16) = 32(4) = 128$ , giving $k^3 = 8$ and $k = 2$ .

2026: 21 May Shift 1

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ m & 2 & n \end{bmatrix}$ is a matrix, such that $AA^T = 9I_3$ , then the values of $m$ and $n$ are (where $I_3$ is an identity matrix of order 3)

2026: 21 May Shift 1

Which of the following matrices are invertible?

(A) $\begin{bmatrix} 2 & 2 \\ 3 & 3 \end{bmatrix}$

(B) $\begin{bmatrix} 2 & 3 \\ 3 & 2 \end{bmatrix}$

(D) $\begin{bmatrix} 3 & 3 \\ 3 & 3 \end{bmatrix}$

Choose the correct answer from the options given below:

2022: 17 Aug Shift 2

Match List - I with List - II.

List - I	List - II
(A) $A$ is a square matrix of order $3$ and $\lvert 2A \rvert = k\lvert A \rvert$ , then $k$ is	(I) $0$
(B) Value of $\begin{vmatrix}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{vmatrix}$ is	(II) $3$
(C) Matrix $\begin{bmatrix}5-x & x+1 \\ 2 & 4\end{bmatrix}$ is singular, then $x =$	(III) $8$
(D) If $A = (a_{ij}) = \begin{bmatrix}5 & 3 & 8 \\ 2 & 0 & 1 \\ 1 & 2 & 3\end{bmatrix}$ , then the minor of the element $a_{23}$ is	(IV) $7$

Choose the correct answer from the options given below :

2025: 22 May Shift 2

If $P\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} = \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix}$ , then matrix P is equal to:

2025: 15 May Shift 2

The following system of equations $2x - y + 3z = 5, 3x + 2y - z = 7, 4x + 5y - \lambda z = \mu$ is consistent. Then

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:

If A is a matrix of order 3×33 \times 33×3 such that ∣A∣=4|A| = 4∣A∣=4 and ∣k⋅adj A∣=32∣A∣,k∈R|k \cdot adj\, A| = 32|A|, k \in \mathbb{R}∣k⋅adjA∣=32∣A∣,k∈R; then the value of k is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If A is a matrix of order $3 \times 3$ such that $|A| = 4$ and $|k \cdot adj\, A| = 32|A|, k \in \mathbb{R}$ ; then the value of k is: