7 The matrix \(\mathbf { A }\) is given by
$$A = \left( \begin{array} { r r r }
- 6 & 2 & 13
0 & - 2 & 5
0 & 0 & 8
\end{array} \right) .$$
- Find a matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { A } ^ { - 1 } = \mathbf { P D P } ^ { - 1 }\).
- Use the characteristic equation of \(\mathbf { A }\) to find \(\mathbf { A } ^ { - 1 }\).