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## 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!