6 The matrix \(\mathbf { A }\) is given by
$$A = \left( \begin{array} { r r r }
5 & - \frac { 22 } { 3 } & 8
0 & - 6 & 0
0 & 0 & 1
\end{array} \right)$$
- Find a matrix \(\mathbf { P }\) and a diagonal matrix \(\mathbf { D }\) such that \(\mathbf { A } ^ { 2 } = \mathbf { P D P } ^ { - 1 }\).
- Use the characteristic equation of \(\mathbf { A }\) to find \(\mathbf { A } ^ { 3 }\).