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Math Help - Proof help (lin. algebra ?)

  1. #1
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    Proof help (lin. algebra ?)

    Okay so I was practicing proofs and the following appeared in my book. i'm confused as to how do it so i would be thankful for any help:

    Let A be a symmetric nonsingular matrix. Prove that its inverse (A^-1) is symmetric.
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  2. #2
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    Quote Originally Posted by buckaroobill View Post
    Okay so I was practicing proofs and the following appeared in my book. i'm confused as to how do it so i would be thankful for any help:

    Let A be a symmetric nonsingular matrix. Prove that its inverse (A^-1) is symmetric.
    Let * mean transpose.

    We know that,
    A*=A
    Because it is symettric.

    We need to show,
    (A^-1)*=A^-1 (1)

    You can use the fact that,
    (M^-1)*=(M*)^-1
    For non-singular matrices.

    But that means in (1) we have,
    (A^-1)*=(A*)^-1=A^-1
    Thus, it is symmettric.
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