I am given that $A$ is an $m$ by $m$ matrix and that $A$ and $A^{-1}$ are both filled with integer values. How can I find all possible values of the determinant of $A$?

I tried solving this by stating $det(AA^{-1})=1$. Then $det(A)det(A^{-1})=1$ and $det(A)= det(A^{-1})^{-1}$. However, when simplified, this just gives me $det(A)= det(A)$.

Any guidance is much appreciated!