7 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { c c } a & 3
- 2 & 1 \end{array} \right)\).
- Given that \(\mathbf { A }\) is singular, find \(a\).
- Given instead that \(\mathbf { A }\) is non-singular, find \(\mathbf { A } ^ { - 1 }\) and hence solve the simultaneous equations
$$\begin{aligned}
a x + 3 y & = 1
- 2 x + y & = - 1
\end{aligned}$$