Algebra

Matrices & Determinants

Easy

common

If A is a square matrix of order 3, B = kA and |B| = $x$ |A| then,

$x = 2k$

$x = k^2$

$x = k^3$

$x = 3k$

✅ Correct Option: 3

For a square matrix of order $n$ , $|kA| = k^n |A|$ . Here $n=3$ , so $|B| = |kA| = k^3 |A|$ . Comparing with $|B| = x|A|$ gives $x = k^3$ .

2025: 21 May Shift 2

If $x, y$ and $z$ are non-zero distinct numbers, then $\begin{vmatrix} x+y & y+z & z+x \\ z & x & y \\ 1 & 1 & 1 \end{vmatrix}$ is equal to

2026: 18 May Shift 1

The maximum value of $\Delta = \begin{vmatrix}1 & \sin\theta & 1\\ -\sin\theta & 1 & \sin\theta\\ -1 & -\sin\theta & 1\end{vmatrix}$ is ( $\theta$ is real number)

2023: 22 May Shift 3

The value of the determinant $\Delta = \begin{vmatrix} 1! & 2! & 3! \\ 2! & 3! & 4! \\ 3! & 4! & 5! \end{vmatrix}$ is :

2026: 30 May Shift 2

A is a square matrix of order 3 x 3, then

Match List-I with List-II

List-I	List-II
(A) $\left\vert \text{adj}A \right\vert$	(I) $\dfrac{1}{\left\vert A \right\vert}$
(B) $\left\vert A^{-1} \right\vert$	(II) $\left\vert A \right\vert^{4}$
(C) $\left\vert A.\text{adj}A \right\vert$	(III) $\left\vert A \right\vert^{3}$
(D) $\left\vert \text{adj}(\text{adj}A) \right\vert$	(IV) $\left\vert A \right\vert^{2}$

Choose the correct answer from the options given below:

2026: 22 May Shift 2

If $f(x) = \begin{vmatrix} 0 & x+a & x+b \\ x-a & 0 & x+c \\ x-b & x-c & 0 \end{vmatrix}$ then the value of $f(0)$ is equal to:

2025: 29 May Shift 2

The inverse of the matrix $\begin{bmatrix} 4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6 \end{bmatrix}$ is

If A is a square matrix of order 3, B = kA and |B| = xxx|A| then,

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If A is a square matrix of order 3, B = kA and |B| = $x$ |A| then,