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Math Help - singular matrices prove

  1. #1
    MHF Contributor
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    singular matrices prove

    A,B are matrices of nXn order. n is odd number.
    prove that if AB+BA=0 then at least one matrices is singular (non invertible).

    how i tried to solve it:
    suppose A and B is invertible
    and AB+BA=0 -> AB=-BA
    so by multiplying A^-1 from left on both sides
    B=- A^-1BA

    what to do now
    ?
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  2. #2
    Super Member girdav's Avatar
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    re: singular matrices prove

    When you have AB=-BA, compute the determinant on both sides.
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  3. #3
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    re: singular matrices prove

    i am not i cand do that
    we cant put determinant on both sides
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  4. #4
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    Given the phrasing of the problem it's clear they want you to use the properties of determinants.

    Use the two properties:
    \det(AB)=\det(A)\det(B)
    \det(cA)=c^{n}\det(A)

    Quote Originally Posted by transgalactic View Post
    i am not i cand do that
    we cant put determinant on both sides
    What do you mean? Are you specifically not allowed to use determinants?
    Last edited by mr fantastic; June 26th 2011 at 03:42 AM. Reason: Merged posts.
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