In each case given below, find :

(a) the order of matrix M.

(b) the matrix M.

(i) $M \times \begin{bmatrix$}[r] 1 & 1 \ 0 & 2 \end{bmatrix} =\begin{bmatrix}[r] 1 & 2 \end{bmatrix}

(ii) $\begin{bmatrix$}[r] 1 & 4 \ 2 & 1 \end{bmatrix} \times M = \begin{bmatrix}[r] 13 \ 5 \end{bmatrix}

If A = $\begin{bmatrix$}[r] 2 & x \ 0 & 1 \end{bmatrix} \text{and } B = \begin{bmatrix}[r] 4 & 36 \ 0 & 1 \end{bmatrix}; find the value of x, given that : A² = B.

Given A = $\begin{bmatrix$}[r] 3 & 0 \ 0 & 4 \end{bmatrix}, B = \begin{bmatrix}[r] a & b \ 0 & c \end{bmatrix} and that AB = A + B; find the values of a, b and c.

If A = $\begin{bmatrix$}[r] 2 & 1 \ 1 & 3 \end{bmatrix} \text{ and } B = \begin{bmatrix}[r] 3 \ -11 \end{bmatrix} find the matrix X such that AX = B.