Let $B$ be an $n \times n$ matrix. Does $B^3 = O_n$ imply $B = O_n$? If so, why?
2026-03-25 20:59:50.1774472390
If $B^3 = O$ does it mean that $B = O$?
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No, take the matrix $$ \begin{pmatrix}0 &\ldots &0 &1 &0 \\ \vdots & & &0 &1 \\ \vdots & & & &0 \\ \vdots & & & &\vdots \\ 0 &\ldots &\ldots &\ldots &0 \end{pmatrix} $$