(a) If $A = \begin{bmatrix} 1 & 2 & -3 \\ 2 & 0 & -3 \\ 1 & 2 & 0 \end{bmatrix}$, then find $A^{-1}$ and hence solve the following system of equations : $x + 2y - 3z = 1$, $2x - 3z = 2$, $x + 2y = 3$