Algebra

Matrices & Determinants

Easy

If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{1}{4}$

$\frac{3}{4}$

✅ Correct Option: 3

For a skew symmetric matrix, all diagonal elements are zero. Setting diagonal entries to zero: $2x-1=0 \Rightarrow x=1/2$ , $3y-2=0 \Rightarrow y=2/3$ , $4z-3=0 \Rightarrow z=3/4$ . Therefore $xyz = (1/2)(2/3)(3/4) = 1/4$ .

2026: 25 May Shift 1

If $\begin{vmatrix} 2x & 2 \\ 8 & x \end{vmatrix} = \begin{vmatrix} -4 & -2 \\ 4 & -2 \end{vmatrix}$ then $x =$

2022: 23 Aug Shift 1

If $A^2 - A + I = O$ , where O is the zero matrix and I is the identity matrix, then $A^{-1}$ is

2025: 15 May Shift 2

If A and B are symmetric matrices of the same order, then

2026: 22 May Shift 2

Which of the following statements are true?

(A) A matrix which is both symmetric as well as skew-symmetric is a null matrix.

(B) All positive integral powers of a symmetric matrix are symmetric.

(D) All positive even integral powers of a skew-symmetric matrix are skew-symmetric.

Choose the correct answer from the options given below:

2025: 14 May Shift 1

If A and B are skew-symmetric matrices, then which one of the following is NOT true?

2026: 29 May Shift 1

Match List-I with List-II

List-I (Singular matrix)	List-II (A value of $x$ )
(A) $A=\begin{bmatrix}x & 4 \\ 2 & 2x\end{bmatrix}$	(I) 3
(B) $A=\begin{bmatrix}3 & x \\ 3x & 9\end{bmatrix}$	(II) 4
(C) $A=\begin{bmatrix}x & 1 \\ 1 & x\end{bmatrix}$	(III) 2
(D) $A=\begin{bmatrix}x & 1 \\ 16 & x\end{bmatrix}$	(IV) 1

Choose the correct answer from the options given below:

If [2x−1−3633y−24−6−44z−3]\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}​2x−13−6​−33y−2−4​644z−3​​ is skew symmetric matrix, then xyzxyzxyz is equal to

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to