2 The matrix \(\mathbf { A }\) is given by \(\mathbf { A } = \left( \begin{array} { r r c } 2 & 1 & 2
1 & - 1 & 1
2 & 2 & a \end{array} \right)\).

1. Show that \(\operatorname { det } \mathbf { A } = 6 - 3 a\).
2. State the value of \(a\) for which \(\mathbf { A }\) is singular.
3. Given that \(\mathbf { A }\) is non-singular find \(\mathbf { A } ^ { - 1 }\) in terms of \(a\).