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 $\det(A) = ±1.$ I have no idea how to solve this. One of the hints is that I "can use the classical adjoint of $A$"

There is a formula of $A^{-1}$ with cofactor matrices https://en.wikipedia.org/wiki/Minor_%28linear_algebra%29#Inverse_of_a_matrix
