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Math Help - Show that if M is invertible, M^t is also invertible

  1. #1
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    Show that if M is invertible, M^t is also invertible

    hmm, how do i prove this one?

    plus,

    (M^t)^-1 = (M^-1)^t
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by experiment00 View Post
    hmm, how do i prove this one?

    plus,

    (M^t)^-1 = (M^-1)^t

    from
    A^T(A^{-1})^T=(A^{-1}A)^T=I^T = I
    we conclude that it's really
    (A^{-1})^T=(A^T)^{-1}
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  3. #3
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    if M is invertible, then \det(M)\neq 0

    \because~\det(M^T)=\det(M)\neq 0, so M^T is invertible
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