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Math Help - does this mean a matrix is singular?

  1. #1
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    does this mean a matrix is singular?

    If a matrix A \neq 0 and A^k=0 where k is a positive integer, does that mean A is singular?
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  2. #2
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    A must be singular. Suppose not, then there exists A^{-1} satisfying AA^{-1}=A^{-1}A = I. Then A^k (A^{-1})^k = I = 0, giving a contradiction.
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  3. #3
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    so the =0 means a matrix full of zeros right?
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  4. #4
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    Quote Originally Posted by superdude View Post
    so the =0 means a matrix full of zeros right?
    Yes, that is the 0 matrix.
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