CUET Mathematics 2025 26 May Shift 2 PYQs

Let A be any skew- symmetric matrix (where $A^T$ is Transpose of matrix A). Then which of the following statements are correct?

(A) $A^2$ is a symmetric matrix

(B) $A^2$ is a skew- symmetric matrix

(C) $A^T A = -A^2$

(D) $A^T A - AA^T = O$

Choose the correct answer from the options given below:

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

Consider the matrices $A = \begin{bmatrix} 9 & 0 & 0 \\ 0 & 16 & 0 \\ 0 & 0 & 25 \end{bmatrix}$ and $B = \begin{bmatrix} \frac{1}{5} & 0 & 0 \\ 0 & \frac{1}{4} & 0 \\ 0 & 0 & \frac{1}{3} \end{bmatrix}$. The value of $|(AB)^{-1}|$ is