Matrices Test -...

If $$A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1\end{bmatrix}$$, then $$A^2$$ is equal to 

If $$A = \begin{bmatrix}3 & 1 \\ -1 & 2\end{bmatrix}$$, Then $$A^2$$ = 

If $$\displaystyle A=\begin{bmatrix}x &y \\z  &w \end{bmatrix},B=\begin{bmatrix}x &-y \\-z  &w \end{bmatrix}$$ and $$C=\begin{bmatrix}-2x &0 \\0  &-2w \end{bmatrix},$$ then $$A+B+C$$ is a:

If $$\begin{bmatrix}3 & -1 \\ 2 & 5\end{bmatrix}\begin{bmatrix}x \\ y \end{bmatrix} = \begin{bmatrix}4 \\ -3\end{bmatrix},$$ find $$x$$ and $$y$$

If $$\displaystyle \:A= \left [ \begin{matrix}4 &x+2 \\2x-3  &x+1 \end{matrix} \right ]$$ is symmetric, then x= 

If $$\displaystyle A=\left [ a_{ij} \right ]_{m\times\:n}, B=\left [ b_{ij} \right ]_{m\times\:n},$$ then the element $$\displaystyle C_{23}$$ of the matrix $$C=A+B$$ is 

If $$A-A'=0$$, then $$A'$$ is

For any square matrix $$A,  \  A+{A}^{T}$$ is-

If $$\displaystyle  \begin{bmatrix} x & y   \\ 1 & 6   \end{bmatrix} $$ = $$\displaystyle  \begin{bmatrix} 1 & 8   \\ 1 & 6   \end{bmatrix},$$ then $$x+2y=$$

Given that $$\displaystyle M=\begin{bmatrix}3 &-2 \\-4  &0 \end{bmatrix}\:and\:N=\begin{bmatrix}-2 &2 \\5  &0 \end{bmatrix}$$, then $$M+N$$ is a