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This is one of the three linear algebra scholarship questions given by my university last year. I've solved the other two, but this one is posing a bit of a problem. Question 1 on the file.

Given that for a nxn matrix A both matricies A and A^{-1}have integer entries, show that det(A) = +-1

2. Relevant equations

3. The attempt at a solution

I'm completely lost. I have a feeling co-factor expansion isn't the way to go, as that would be very messy, and the other two worked out fairly nicely when you know what you're doing.

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# Linear Algebra scholarship exam

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