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Math Help - Find nilpotent

  1. #1
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    Find nilpotent

    Find two nilpotent 2 by 2 matrices such that their sum is not nilpotent.

    I have been trying a few matrices but none are working, is there a more logical, easier way to find these matrices? thanks.
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    are nilpotent, but their sum,
    01
    10
    is inversible so it is not nilpotent
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    So inversible means no nilpotent? How so? Thanks.
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    Quote Originally Posted by tttcomrader View Post
    So inversible means no nilpotent? How so? Thanks.
    Because if A is invertible then A^n is invertible. Thus, if A^n is not invertible then A is not invertible. If A^n is zero matrix then it means A^n is not invertible and so A is not invertible.
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    Quote Originally Posted by ThePerfectHacker View Post
    Because if A is invertible then A^n is invertible. Thus, if A^n is not invertible then A is not invertible. If A^n is zero matrix then it means A^n is not invertible and so A is not invertible.
    Thank you TPH, you just answered a question of mine. I'm glad I've searched into the forum.
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