\(\mathbf { 9 }\) The matrix \(\mathbf { X }\) is given by \(\mathbf { X } = \left( \begin{array} { r r r } a & 2 & 9
2 & a & 3
1 & 0 & - 1 \end{array} \right)\).
- Find the determinant of \(\mathbf { X }\) in terms of \(a\).
- Hence find the values of \(a\) for which \(\mathbf { X }\) is singular.
- Given that \(\mathbf { X }\) is non-singular, find \(\mathbf { X } ^ { - 1 }\) in terms of \(a\).