Matrices Test -...

If $$A=[x\, y\, z], B = \begin{bmatrix}a&h&g\\h&b&f\\g&f&c\end{bmatrix}$$ and $$C=\begin{bmatrix}x\\y\\z\end{bmatrix}$$
Then, $$ABC = 0$$, if

$$A=\begin{bmatrix} -2&4\\-1&2  \end{bmatrix}$$, then $$A^2$$ is equal to 

If $$P=\begin{pmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{pmatrix}$$, then $${P}^{5}$$ is equal to

If $$A =\begin{bmatrix} 2 & -1 \\ -1 & 2  \end{bmatrix}$$ and $$I$$ is the unit matrix of order $$2$$, then $$A^2$$ equals

If $$A$$ is a matrix such that $$\begin{pmatrix}2&1 \\3&2 \end{pmatrix} A(1 \space  \,1)=\begin{pmatrix}1&1 \\0&0 \end{pmatrix}$$ then $$A= $$

If $$A$$ and $$B$$ are any two matrices, then 

For the matrices $$A=\begin{bmatrix} 1 & 3 \\ 0 & -1 \end{bmatrix}$$ $$B=\begin{bmatrix} 2 & 2 \\ -1 & 4 \end{bmatrix}$$
What is $$AB$$?

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

$$\begin{bmatrix} 3& 2\\ -1 & -2\\ 4 & 5\end{bmatrix} \begin{bmatrix} 0& a\\ b & c \end{bmatrix} = \begin{bmatrix}-4 &9 \\ 4 & -7\\ -10 & 19\end{bmatrix}$$
Find $$a, b$$ and $$c$$.

If $$P=\begin{pmatrix}2&-2&-4 \\-1&3&4\\1&-2&-3\end{pmatrix}$$ then $$P^5$$ equals