If the matrix bmatrix0 & & 2\\2 & & 1\\ & -1 & 0bmatrix is skew-symmetric, then (--) equals Option 1: 1 Option 2: 9 Option 3: 4 Option 4: 2

Answer: 4. Solution: Skew symmetry requires zero diagonal, so =0; also a_12=-a_21 gives =-2, and a_13=-a_31 gives =-2. Hence --=0+2+2=4.

Algebra

Matrices & Determinants

Easy

applied

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals

✅ Correct Option: 3

Skew symmetry requires zero diagonal, so $\beta=0$ ; also $a_{12}=-a_{21}$ gives $\alpha=-2$ , and $a_{13}=-a_{31}$ gives $\gamma=-2$ . Hence $\beta-\alpha-\gamma=0+2+2=4$ .

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: 16 May Shift 1

If A is a square matrix of order 3 and |A| = -5, then |3A| is equal to

2026: 29 May Shift 1

If $A=\begin{bmatrix} x & p & x+p \\ y & q & y+q \\ z & r & z+r \end{bmatrix}$ , then $|A|$ is

2025: 27 May Shift 1

If A is a square matrix such that $A^2 = A$ and I is the identity matrix of the same order as A, then $(I+A)^2-3A$ is equal to

2025: 22 May Shift 2

If $A = \begin{bmatrix} x & 3 \\ 2 & 4 \end{bmatrix}$ , $B = \begin{bmatrix} 2 & 3 \\ y & 3 \end{bmatrix}$ and $C = \begin{bmatrix} z & 1 \\ 8 & 2 \end{bmatrix}$ are singular matrices then:

(A) $x > y$

(B) $y > z$

(D) $x \neq y \neq z$

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?

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

If the matrix [0α22β1γ−10]\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}​02γ​αβ−1​210​​ is skew-symmetric, then (β−α−γ)(\beta-\alpha-\gamma)(β−α−γ) equals

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals