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Math Help - Linear Algebra Proof with invertible matrices

  1. #1
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    Linear Algebra Proof with invertible matrices

    I don't even know where to start with this:

    Let A be an n x n invertible matrix. Prove that AT is invertible and determine its inverse in terms of A-1.

    Any hints or suggestions would be appreciated!
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  2. #2
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    Re: Linear Algebra Proof with invertible matrices

    We know A is invertible, and so A^{-1}A=I

    Taking the transpose of both sides gives A^T(A^{-1})^T=I

    What can you then conclude about the invertibility of A^T?
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  3. #3
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    Re: Linear Algebra Proof with invertible matrices

    So then can I just say, since these two are equal A transpose is invertible. Then it's inverse is A inverse times A.
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  4. #4
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    Re: Linear Algebra Proof with invertible matrices

    Quote Originally Posted by widenerl194 View Post
    So then can I just say, since these two are equal A transpose is invertible. Then it's inverse is A inverse times A.
    No, A^{-1}A= I, not (A^T)^{-1}.

    What you can say is that the inverse of A transpose is the transpose of A inverse.
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