I got the matrix A
3 2 -1
1 6 3
2 -4 0
I'm not sure if determinants are always positive, but they must be because in my textbook, the determinant is 64.
I got this calculating the minors of row 1. I got 36+12+16. For row 2 I got -4-12-48 and row 3 I got 24-40+0.
This leads me to believe dets are always positive, but I'm not sure. What are the conditions for the sign of determinants?