# linear algebra – Find all possible values of the determinant of matrix \$A\$

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!