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Math Help - proof involving inverses of invertible matrices

  1. #1
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    proof involving inverses of invertible matrices

    Let A be an nxn invertible matrix.

    I can't figure out how to prove the following:

    t(A^-1) = (t(A))^-1. So the transpose of A inverse is equal to the inverse of A transpose.
    Last edited by grandunification; September 17th 2009 at 03:47 PM.
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  2. #2
    Member courteous's Avatar
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    So, if I understand, you wonder if equality (A^{-1})^T=(A^T)^{-1} holds.

    Multiply both sides by A^T: (A^{-1})^TA^T=(A^T)^{-1}A^T.
    On the right-hand side of the equation you have identity matrix: (A^{-1})^TA^T=I.
    And left-side, (A^{-1})^TA^T, equals identity matrix (A(A^{-1}))^T=I.

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  3. #3
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    Ya, I just worked it out right before I checked your answer. Thanks anyways though.
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