Solution MM.C33 Chris Black

We quickly compute $A^2 = \begin{bmatrix} 0 & 0 & 1\\ 0 & 0 & 0\\ 0 & 0 & 0\end{bmatrix}$, and we then see that $A^3$ and all subsequent powers of $A$ are the $3 \times 3$ zero matrix; that is, $A^n = \zeromatrix_{3,3}$ for $n\ge 3$.