If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$,then ${A^2} = $

If $A = \begin{bmatrix} a & b \\ c & -a \end{bmatrix}$ is such that $A^2 = I$, then . . . . . . .

If $A = \begin{bmatrix} 4 & 2 \\ -1 & 1 \end{bmatrix}$ and $I$ is the identity matrix of order $2$,then $(A - 2I)(A - 3I) = $

If a matrix $A$ is both symmetric and skew-symmetric,then

The matrix $A = \begin{bmatrix} 1 & -3 & -4 \\ -1 & 3 & 4 \\ 1 & -3 & -4 \end{bmatrix}$ is nilpotent of index:

If $A = \frac{1}{\pi} \begin{bmatrix} \sin^{-1}(x\pi) & \tan^{-1}(\frac{x}{\pi}) \\ \sin^{-1}(\frac{x}{\pi}) & \cot^{-1}(\pi x) \end{bmatrix}$ and $B = \begin{bmatrix} -\frac{1}{\pi} \cos^{-1}(x\pi) & \frac{1}{\pi} \tan^{-1}(\frac{x}{\pi}) \\ \frac{1}{\pi} \sin^{-1}(\frac{x}{\pi}) & -\frac{1}{\pi} \tan^{-1}(\pi x) \end{bmatrix}$,then $A-B$ is equal to: