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Transposing and Inversing Matrices

  1. Sep 16, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that if A is an invertible matrix, then A*AT and AT*A are also invertible.


    2. Relevant equations
    (AT)-1=(A-1)T
    (AB)T=ATBT

    3. The attempt at a solution
    I just can't wrap my brain around this one. I know that I have to multiply a matrix by its inverse to get the identity matrix, but I don't know where to go from there.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2008 #2

    Dick

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    Science Advisor
    Homework Helper

    (AB)^T=B^T*A^T. Not A^T*B^T. Now that we've gotten past that, what would be the inverse of A*A^T given both of the elements in the product have inverses?
     
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