Let $A$ be a $3 \times 3$ matrix having entries from the set $\{-1, 0, 1\}$. The number of all such matrices $A$ having the sum of all the entries equal to $5$ is:

Assume $X, Y, Z, W$ and $P$ are matrices of order $2 \times n, 3 \times k, 2 \times p, n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7X - 5Z$ is

The number of all $3 \times 3$ matrices $A$,with entries from the set $\{-1, 0, 1\}$ such that the sum of the diagonal elements of $AA^{T}$ is $3$,is

If $A = \begin{bmatrix} 1 & 0 \\ -1 & 7 \end{bmatrix}$,$I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A^{2} = 8A + kI$,then the value of $k$ is

If $M = \begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}$ and $M^2 - \lambda M - I_2 = 0$,then $\lambda = $

Let $\alpha, \beta, \gamma$ be real numbers. If $\begin{bmatrix} 7 & 5 & \alpha \\ \beta & 2 & 11 \\ 3 & \gamma & 1 \end{bmatrix} \begin{bmatrix} 1 \\ 3 \\ 2 \end{bmatrix} = \begin{bmatrix} \alpha+\beta \\ -2\alpha+\beta-2\gamma \\ \alpha+2\beta+3\gamma \end{bmatrix}$, then find the value of $100+\frac{2\alpha+11\beta}{\gamma}$.