Let $A$ be $n\times n$ matrix. Prove that if $A^2=\mathbf{0}$ then $A$ is not invertible.
Prove that if $A^2=0$ then $A$ is not invertible
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linear-algebra
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9Please don't order the group around. If you have a question, ask a question. – 2011-02-15
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11I suppose it would be too late to ask everybody not to post complete answers to homework questions... – 2011-02-15
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2Here $n$ should be positive, for otherwise the statement is false. – 2011-02-15
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0@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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0@Mariano: Right. I confused myself - sorry. Thank you for your explanation. – 2011-03-12