How do I prove that if $A$ is a $n\times n$ matrix with integer entries, then $A^{−1}$ has integer entries if and only if $\det(A) = ±1.$

Question

I have no idea how to solve this. One of the hints is that I "can use the classical adjoint of $A$"

What do you know about the classical adjoint? Do you know that $$A^{-1}=\frac1{\det A}(\text{Adj},A) ?$$ — DonAntonio, Apr 06 '16 at 22:26

score 0 · Answer 1 · answered Apr 06 '16 at 22:27

0

answered Apr 06 '16 at 22:27

Tsemo Aristide

1 Answers1