4 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { r r r } 2 & 1 & 2
1 & - 1 & 1
2 & 2 & a \end{array} \right)\).
- Show that \(\operatorname { det } \mathbf { A } = 6 - 3 a\).
- State the value of \(a\) for which \(\mathbf { A }\) is singular.
- Given that \(\mathbf { A }\) is non-singular find \(\mathbf { A } ^ { - 1 }\) in terms of \(a\).