Show that two matrices can be diagonalized

Prove that the matrices $A = \begin{bmatrix} 5 & 6 & 0 \\ -3 & -4 & 0 \\ -2 & 0 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & -1 & 2 \\ -10 & 6 & -14 \\ -6 & 3 & -7 \end{bmatrix}$ are similar. Show that both can be diagonalized and give matrices $P$ and $Q$ such that $P^{-1}AP$ and $Q^{-1}BQ$ are diagonal.

Let $P = \begin{bmatrix} -1 & -2 & 0 \\ 5 & 6 & 1 \\ -1 & -1 & 0 \end{bmatrix}$ and $Q = \begin{bmatrix} 2 & -1 & 3 \\ -1 & 1 & -2 \\ -2 & 1 & -2 \end{bmatrix}$. Evidently we have $P^{-1}AP = Q^{-1}BQ = \begin{bmatrix} -1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 2 \end{bmatrix}$. In particular, $A$ and $B$ are similar and both are diagonalizable.