Appeared in: 2025 (2 sets)
(a) Given $A = \begin{bmatrix} -4 & 4 & 4 \\ -7 & 1 & 3 \\ 5 & -3 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & -1 & 1 \\ 1 & -2 & -2 \\ 2 & 1 & 3 \end{bmatrix}$, find $AB$. Hence, solve the system of linear equations:
$x - y + z = 4$
$x - 2y - 2z = 9$
$2x + y + 3z = 1$
OR
(b) If $A = \begin{bmatrix} 1 & 2 & 0 \\ -2 & -1 & -2 \\ 0 & -1 & 1 \end{bmatrix}$, then find $A^{-1}$.
Hence, solve the system of linear equations:
$x - 2y = 10$
$2x - y - z = 8$
$-2y + z = 7$