If the determinate is 1 the inverse will contain only integers. There's a start.
Also if the determinate divides every value in the matrix the inverse will be full of integers.
I'm trying to come up with examples for my students to do in preparation for an upcoming test. We're not allowing them to use calculators, so the examples need to be relatively easy to compute by hand.
In particular, I'm trying to come up with an algorithm to generate a matrix of integers whose inverse is also a matrix of integers. Anyone have any ideas?