Rational and Jordan canonical forms

Let $A$ be the $4 \times 4$ matrix

A = [\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ - 2 & - 2 & 0 & 1 \\ - 2 & 0 & - 1 & - 2 \end{matrix}] .

Show that the invariant factors of $A$ are $a_{1} (x) = x - 1$ , $a_{2} (x) = (x - 1) (x + 1)^{2}$ .
Determine the rational canonical form $R$ of $A$ and find a change-of-basis matrix $P$ such that $P^{- 1} A P = R$ .
Determine the Jordan canonical form $J$ of $A$ . (Optionally: find a change-of-basis matrix $Q$ such that $Q^{- 1} A Q = J$ .)