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.)
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