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Proving Determinants

  • #1

Homework Statement



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

Homework Equations





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!
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
47
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.
 
  • #3
Thanks! I was making the problem harder than it is!
 

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