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Nxn Matrix AB=I?

  1. Feb 19, 2014 #1

    sheldonrocks97

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    Gold Member

    1. The problem statement, all variables and given/known data

    Prove that every n x n matrix A for which there exists an n x n matrix B such that AB = I must be invertible. Hint: Use properties of determinants.

    2. Relevant equations

    None that I am aware of.

    3. The attempt at a solution

    I tried finding the inverse of the matrix and multiplying by an elementary matrix. I also tried finding the determinants of a simple matrix and using it's properties but nothing is working :(
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 19, 2014 #2

    pasmith

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    Homework Helper

    You are supposed to use the fact that [itex]\det (AB) = (\det A) (\det B)[/itex].
     
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