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Possible Duplicate:
Units and Nilpotents

Given $A^{2012}=0$ prove that $A+I$ is invertible and find an expression for $(A+I)^{-1}$ in terms of $A$. ($I$ is the identity matrix).

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    On the other hand, if I + A not invertible there is a v so that $0 = (I + A) v$, so $Av = -v, A^{2012}v = v, $ A not nilpotent.2012-05-03
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    @ugoolm If you are asking for help with your MATH 1115 assignment due this monday, you should provide a bit more context and where you are stuck.2012-05-03
  • 0
    I think it would be sufficient with a hint like "Do you remember the proof of the geometric formula?".2012-05-03
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    Please don't do this. There's nothing wrong with a closed question while an impenetrable non-question has no value whatsoever.2012-05-04

4 Answers 4