If $A$ is a $3 \times 4$ matrix and $B$ is a matrix such that $A^{\prime}B$ and $BA^{\prime}$ are both defined,then $B$ is of the type:

If $ 2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $,then the values of $ x $ and $ y $ are:

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

If the matrix $\begin{bmatrix} x & x^2+3x & 5 \\ -2x-6 & x^2 & -4x-2 \\ 5 & x^2+2 & x^3 \end{bmatrix}$ is a symmetric matrix, then the value of $x$ is

The matrix $A^2 + 4A - 5I$,where $I$ is the identity matrix and $A = \begin{bmatrix} 1 & 2 \\ 4 & -3 \end{bmatrix}$,equals:

Given $3\begin{bmatrix} x & y \\ z & w \end{bmatrix} = \begin{bmatrix} x & 6 \\ -1 & 2w \end{bmatrix} + \begin{bmatrix} 4 & x+y \\ z+w & 3 \end{bmatrix}$,find the values of $x, y, z$ and $w$.