## Example of a Nilpotent Matrix $A$ such that $A^2\neq O$ but $A^3=O$.

## Problem 305

Find a nonzero $3\times 3$ matrix $A$ such that $A^2\neq O$ and $A^3=O$, where $O$ is the $3\times 3$ zero matrix.

(Such a matrix is an example of a **nilpotent matrix**. See the comment after the solution.)