5. \(\mathbf { A } = \left( \begin{array} { c c } a & - 5
2 & a + 4 \end{array} \right)\), where \(a\) is real.
- Find \(\operatorname { det } \mathbf { A }\) in terms of \(a\).
- Show that the matrix \(\mathbf { A }\) is non-singular for all values of \(a\).
Given that \(a = 0\),
- find \(\mathbf { A } ^ { - 1 }\).