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