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Math Help - If matrix A is invertible then so it it transpose A^t

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    If matrix A is invertible then so it it transpose A^t

    How do I prove or show this? Not sure how to go about it.
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  2. #2
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    If you can prove that both: A^T \left(A^{-1}\right)^T = \left(A^{-1}\right)^T A^T = I

    then by definition, we've shown that A^T is invertible.

    So for: A^T \left(A^{-1}\right)^T = I

    Use the fact that: X^TY^T = (YX)^T

    So we see that: A^T\left(A^{-1}\right)^T = \left(A^{-1}A\right)^T = I^T = I

    Now finish off by proving the other.
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