If $A = \begin{bmatrix} 1 & 2 \\ 3 & 5 \end{bmatrix}$ and $\alpha, \beta \in \mathbb{R}$ are such that $\alpha A^2 - \beta A = 2I$, then $\alpha^2 + \beta =$

If $A = \begin{bmatrix} i & 0 \\ 0 & i \end{bmatrix}$,then ${A^2} = $

If $A = \begin{bmatrix} \frac{2}{3} & 1 & \frac{5}{3} \\ \frac{1}{3} & \frac{2}{3} & \frac{4}{3} \\ \frac{7}{3} & 2 & \frac{2}{3} \end{bmatrix}$ and $B = \begin{bmatrix} \frac{2}{5} & \frac{3}{5} & 1 \\ \frac{1}{5} & \frac{2}{5} & \frac{4}{5} \\ \frac{7}{5} & \frac{6}{5} & \frac{2}{5} \end{bmatrix}$,then compute $3A - 5B$.

If $X_{4 \times 3}$, $Y_{4 \times 3}$ and $P_{2 \times 3}$ are matrices, then the order of the matrix $\left[P(X^T Y)^{-1} P^T\right]^T$ is

If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{100} = $ . . . . . . .

$A = [a_{ij}]_{m \times n}$ is a square matrix,if