If $A$ and $B$ are two matrices such that $A+B$ and $AB$ are both defined,then

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

If $A=\left[\begin{array}{rr}i & -i \\ -i & i\end{array}\right]$ and $B=\left[\begin{array}{rr}1 & -1 \\ -1 & 1\end{array}\right]$, then find $A^8$. (in $B$)

Let $A = [a_{ij}]$ be a $3 \times 3$ matrix such that $A \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}$,$A \begin{bmatrix} 4 \\ 1 \\ 3 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}$,and $A \begin{bmatrix} 2 \\ 1 \\ 2 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$. Then $a_{23}$ equals:

Let $M = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{bmatrix}$ and $I$ be the identity matrix of order $3$. Then $M^2 - 4M =$

Compute the following: $\left[ {\begin{array}{cc} {{\cos }^2}x & {{\sin }^2}x \\ {{\sin }^2}x & {{\cos }^2}x \end{array}} \right] + \left[ {\begin{array}{cc} {{\sin }^2}x & {{\cos }^2}x \\ {{\cos }^2}x & {{\sin }^2}x \end{array}} \right]$