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Math Help - Proof of (A^-1)^-1 = A

  1. #1
    Member mybrohshi5's Avatar
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    Proof of (A^-1)^-1 = A

    I am studying for my exam on tuesday and my professor in class on friday told us to make sure how to prove this:

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

    Can i get some help proving this in the easiest way possible

    Thanks in advanced!
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  2. #2
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    Quote Originally Posted by mybrohshi5 View Post
    I am studying for my exam on tuesday and my professor in class on friday told us to make sure how to prove this:

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

    Can i get some help proving this in the easiest way possible

    Thanks in advanced!

    As by definition X^{-1} is the inverse of X , we get that \left(A^{-1}\right)^{-1} is the

    inverse of A^{-1} . But we know that AA^{-1}=A^{-1}A=I , and now use uniqueness of inverses...

    Tonio
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