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Math Help - Proof

  1. #1
    Newbie kaylakutie's Avatar
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    Proof

    Not sure how to approach this one.

    Prove (A^{-1})^T = (A^T)^{-1}.
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  2. #2
    Junior Member
    Joined
    Feb 2010
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    that is equivalent to prove that

    ({A}^{-1})^t \cdot {A}^t = I

    Owned by the transpose

    (A \cdot {A}^{-1})^t = I
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  3. #3
    Member
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    Quote Originally Posted by kaylakutie View Post
    Not sure how to approach this one.

    Prove (A^{-1})^T = (A^T)^{-1}.
    Hi there,

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

    Keeping in your mind the fact that I^T = I you get

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

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

    This completes your proof.
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