If P and Q are non-singular square matrices of the same order, then $(PQ^{-1})^{-1}$ equals

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, then $A^2 - 5A$ is equal to : (where $I_2$ is identity matrix of order 2)

If $P\begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} = \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix}$, then matrix P is equal to:

The matrix $X$ in the equation $AX = B$, such that $A = \begin{bmatrix} 1 & 3 \\ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 \\ 0 & 2 \end{bmatrix}$ is given by

If $[2x \quad 4]\begin{bmatrix} x \\ -8 \end{bmatrix} = [0]$, then the value of $x$ is/are

A. $-4$

B. $4$

C. $16$

D. $-16$

Choose the correct answer from the options given below:

If A is a non-singular matrix of order 3, then

Match List-I with List-II

Choose the correct answer from the options given below:

If $A^T = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ and $A^{-1} = \begin{bmatrix} p & q \\ r & s \end{bmatrix}$, then