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Prove that if A is nonsingular then the transpose of A is nonsingular.

  1. Sep 7, 2006 #1
    I haven't written a proof in 8 years. Linear Algebra proofs are going to be the death of me. I honestly don't know where to begin. I read a sort of primer on proof writing, but I could use a human walk through or some help.

    So far, I have:

    there exists a B such that AB = BA = I.


    then sometime later:

    (A^T)B = B(A^T) = I

    Beyond this I have no idea. I'm going to visit my prof tomorrow and see what he has to say. The trouble is, is that his english is fair to poor. A heads up or some honest help would be friendly,
    Thanks.
     
  2. jcsd
  3. Sep 7, 2006 #2
    What happens when you take the transpose of the product of two matrices. That is, what is (AB)^t ?
     
    Last edited: Sep 7, 2006
  4. Sep 7, 2006 #3
    (AB)^T = (B^T)(A^T)

    (A^T)^-1 = (A^-1)^T...you can switch the transpose and inverse.

    Then (A^T)(A^T)^-1 = ...

    Note: You should check those identities, I can't remember if they are correct.
     
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