Using squared matrix to show matrix is not invertible – math.stackexchange.com

Using squared matrix to show matrix is not invertible – math.stackexchange.com

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If $B \in M_{n\times n}(\mathbb{R})$ and $B^2\vec{x} = \vec{0}$ for some vector $\vec{x} \neq \vec{0}$, then $B$ is not invertible. I get that the $rank\space {B^2} < n$ but I can't seem to be ...

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