Let $A, B, C, D$ and $E$ be $n \times n$ matrices,each with non-zero determinant. If $ABCDE=I$,then $C^{-1}=$

If $I$ is a unit matrix,then $3I$ will be

If $I=\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}$ and $P=\begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -2 \end{bmatrix}$,then the matrix $P^{3}+2P^{2}$ is equal to

Suppose $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is a real matrix with non-zero entries,$ad - bc = 0$ and $A^2 = A$. Then,$a + d$ equals

If a matrix has $8$ elements,what are the possible orders it can have?

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: