Problem

The matrix $A$ is given by

$$A=\begin{pmatrix} -6&2&13\\ 0&-2&5\\ 0&0&8 \end{pmatrix}.$$

(a) Find a matrix $P$ and a diagonal matrix $D$ such that $A^{-1}=PDP^{-1}$.

(b) Use the characteristic equation of $A$ to find $A^{-1}$.