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Homework Help: Linear algebra

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Let A and B be invertible matrices such that A^-1 + B^-1 is also invertible. Prove that A+B is invertible.


    2. Relevant equations
    A(A^-1) = I
    B(B^-1) = I
    (A^-1+B^-1)(A^-1+B^-1)^-1 = I

    3. The attempt at a solution
    I've been trying to manipulate these equations to make something work, but I just can't seem to find the right combination.
     
  2. jcsd
  3. Feb 6, 2010 #2
    Haha, me neither. I think we take the same class at the same school XD
     
  4. Feb 7, 2010 #3
    Hint:Try to get A+B by multiplying the terms implied in the problem statement.
     
    Last edited: Feb 7, 2010
  5. Feb 7, 2010 #4
    Thanks Scigatt. Your hint reminds me of a theorem that said "The product of invertible matrices is invertible." It's so simple when you put it like that.
     
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