Chapter 4.4, Problem 41EQ

In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that $P^{-1}AP=B$.

$A=\left[\begin{array}{ccc}1& 0& 2\\ 1& -1& 1\\ 2& 0& 1\end{array}\right],B=\left[\begin{array}{ccc}-3& -2& 0\\ 6& 5& 0\\ 4& 4& -1\end{array}\right]$