Diagonalization and matrix powers

Let $A = [\begin{matrix} 0 & 0 & - 2 \\ 1 & 2 & 1 \\ 1 & 0 & 3 \end{matrix}]$ .

(a) Determine whether $A$ is diagonalizable, and if so, give its diagonal form along with a diagonalizing matrix.
(b) Compute $A^{42}$ . Remember to show all work.

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Let $A=\begin{bmatrix} 0 & 0 & -2 \\ 1 & 2 & 1 \\ 1 & 0 & 3\end{bmatrix}$.
\begin{enumerate}[label=\alph*)]
	\item Determine whether $A$ is diagonalizable, and if so, give its diagonal form along with a diagonalizing matrix.
	\item Compute $A^{42}$. Remember to show all work.
\end{enumerate}