3 The matrix \(\mathbf { A }\) is given by
$$\mathbf { A } = \left( \begin{array} { l l l }
6 & - 9 & 5
5 & - 8 & 5
1 & - 1 & 2
\end{array} \right)$$
- Find the eigenvalues of \(\mathbf { A }\).
- Use the characteristic equation of \(\mathbf { A }\) to show that \(\mathbf { A } ^ { - 1 } = p \mathbf { A } ^ { 2 } + q \mathbf { l }\), where \(p\) and \(q\) are constants to be determined.