CUET Mathematics 2022 7 Aug Shift 2 PYQs

If $A = \begin{bmatrix} 7 & 3 \\ 5 & -7 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals

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:

Which of the following statements are correct ?

(A) $|A'| = |A|$, where A is the transpose of matrix A

(B) If $A = [a_{ij}]_{3 \times 3}$, then $|4A| = 64|A|$

(C) $|A| = |\text{adj } A|^{n-1}$, where n is the order of the matrix

(D) If A is an invertible matrix of order 2, then $\det(A^{-1})$ is equal to $\frac{1}{\det(A)}$

Choose the correct answer from the options given below :