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Math Help - Matrix Inverse Proof

  1. #1
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    Matrix Inverse Proof

    Show that (A ^{-1})^T = (A ^T)^{-1}

    Assuming A is invertible.
    Last edited by Jameson; September 9th 2009 at 01:55 PM.
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  2. #2
    Super Member Matt Westwood's Avatar
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    If you can take the assumption that the determinant of a matrix and its transpose are equal, you can do it by induction and the definition of the inverse as it is defined in terms of cofactors.

    Here's Wikipedia:

    Invertible matrix - Wikipedia, the free encyclopedia

    ... it might help.
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  3. #3
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     A A^{-1} = I

     (A A^{-1})^T = (I)^T

    (A^{-1})^T A^T = I

    By definition of inverse matrix, (A^{-1})^T is the inverse of A^T, hence:

    (A^{-1})^T  =  (A^T)^{-1}
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