If $M$ is a $3 \times 3$ matrix such that $(0\,1\,2) M = (1\,0\,0)$ and $(3\,4\,5) M = (0\,1\,0)$, then $(6\,7\,8) M$ is equal to

If $A=\left[\begin{array}{rrr}1 & 1 & -1 \\ 2 & 0 & 3 \\ 3 & -1 & 2\end{array}\right]$,$B=\left[\begin{array}{rr}1 & 3 \\ 0 & 2 \\ -1 & 4\end{array}\right]$ and $C=\left[\begin{array}{rrrr}1 & 2 & 3 & -4 \\ 2 & 0 & -2 & 1\end{array}\right]$,find $A(BC)$,$(AB)C$ and show that $(AB)C=A(BC)$.

If $A = \begin{bmatrix} 3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3 \end{bmatrix}$,then $A^3 = $ . . . . . . (in $A$)

If $A = \begin{bmatrix} 2 & 2 \\ -3 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $(B^{-1}A^{-1})^{-1} = $

For two $3 \times 3$ matrices $A$ and $B$,let $A + B = 2B^T$ and $3A + 2B = I_3$,where $B^T$ is the transpose of $B$ and $I_3$ is the $3 \times 3$ identity matrix. Then:

Find the value of $x, y$ and $z$ from the following equation : $\begin{bmatrix} 4 & 3 \\ x & 5 \end{bmatrix} = \begin{bmatrix} y & z \\ 1 & 5 \end{bmatrix}$