4. Given that
$$\mathbf { A } = \left( \begin{array} { c c }
k & 3
- 1 & k + 2
\end{array} \right) \text {, where } k \text { is a constant }$$
- show that \(\operatorname { det } ( \mathbf { A } ) > 0\) for all real values of \(k\),
- find \(\mathbf { A } ^ { - 1 }\) in terms of \(k\).