Invertible Matrices with det=1 & Integer Entries: Why Inverse is Integer?

[bodensee9]

Can someone explain why if an invertible matrix A has det = 1 and all integer entries, its inverse also has all integer entries? det(A) = 1 means that if you apply the big formula (permutations) the sums of the entries add up to 1. But what does that have to with having integers in its inverse?

Thanks.

 

[bodensee9]

never mind, figured it out. thanks.