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Let $A$ be $n\times n$ matrix. Prove that if $A^2=\mathbf{0}$ then $A$ is not invertible.

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    Please don't order the group around. If you have a question, ask a question.2011-02-15
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    I suppose it would be too late to ask everybody not to post complete answers to homework questions...2011-02-15
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    Here $n$ should be positive, for otherwise the statement is false.2011-02-15
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    @Rasmus, as the only element in that ring is $0$, every element satisfies the condition that $A^2=0$, but every element is also invertible!2011-03-12
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    @Mariano: Right. I confused myself - sorry. Thank you for your explanation.2011-03-12

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