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Proving Determinants

  1. Oct 27, 2011 #1
    1. The problem statement, all variables and given/known data

    If the entries of A and A^-1 are all integers, how do you know that both determinants are 1 or -1?

    2. Relevant equations



    3. The attempt at a solution

    I know that
    1 = det I = detAA-1=detA * detA-1= detA*(1/detA) = 1
    Not sure how we get to - or the role integers play in it.

    Thanks for your help!
     
  2. jcsd
  3. Oct 27, 2011 #2

    CompuChip

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    Science Advisor
    Homework Helper

    So you have just shown that, if A = A-1, then det A = 1 / det A.
    Now consider the values that det A can take if all entries of A are integers.
     
  4. Oct 27, 2011 #3
    Thanks! I was making the problem harder than it is!
     
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