- Given that
$$\mathbf { A } = \left( \begin{array} { l l }
3 & 2
2 & 2
\end{array} \right)$$
- find the characteristic equation for the matrix \(\mathbf { A }\), simplifying your answer.
- Hence find an expression for the matrix \(\mathbf { A } ^ { - 1 }\) in the form \(\lambda \mathbf { A } + \mu \mathbf { I }\), where \(\lambda\) and \(\mu\) are constants to be found.