Algebra

Matrices & Determinants

Medium

applied

If the matrix $A = \begin{bmatrix} x & -2 & -5y \\ 2 & 0 & -9 \\ 10 & 3z & 0 \end{bmatrix}$ is skew-symmetric, then the value of $(2x - 3y + 4z)$ is :

$-2$

✅ Correct Option: 2

Skew-symmetric: diagonal $= 0$ , so $x = 0$ .

$a_{13} = -a_{31}$ : $-5y = -10 \Rightarrow y = 2$ .

$a_{23} = -a_{32}$ : $-9 = -3z \Rightarrow z = 3$ .

$2x - 3y + 4z = 0 - 6 + 12 = 6$ .

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
A is given matrix	$\left\vert \text{adj}(\text{adj}A) \right\vert$
(A) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 3$	(I) $3$
(B) Order of A $= 3 \times 3$ and $\left\vert A \right\vert = 2$	(II) $1$
(C) Order of A $= 4 \times 4$ and $\left\vert A \right\vert = 1$	(III) $16$
(D) Order of A $= 2 \times 2$ and $\left\vert A \right\vert = 4$	(IV) $4$

Choose the correct answer from the options given below:

2025: 29 May Shift 2

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2025: 3 June Shift 1

If $A = \begin{bmatrix} 5 & 6 \\ 3 & 2 \end{bmatrix}$ then which of the following is correct?

(A) $|A|$ is positive

(B) $|adj\ A| = -8$

(D) $|2A| = -32$

Choose the correct answer from the options given below:

2026: 30 May Shift 1

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If the matrix A=[x−2−5y20−9103z0]A = \begin{bmatrix} x & -2 & -5y \\ 2 & 0 & -9 \\ 10 & 3z & 0 \end{bmatrix}A=​x210​−203z​−5y−90​​ is skew-symmetric, then the value of (2x−3y+4z)(2x - 3y + 4z)(2x−3y+4z) is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the matrix $A = \begin{bmatrix} x & -2 & -5y \\ 2 & 0 & -9 \\ 10 & 3z & 0 \end{bmatrix}$ is skew-symmetric, then the value of $(2x - 3y + 4z)$ is :