Suppose that the $ 3 × 3 $ matrix $A$ has an inverse and each entry of both $A$ and $A^{-1}$ is an integer. What can be the value of the determinant of $A$ ?
I did not understand that what it means that both $A$ and $A^{−1}$ have each entry an integer?
I think that's meant to be $A^{-1}$, not $A-1$. That is, all entries of both the matrix and its inverse are integers.
Hint: the determinant of a matrix of integers is an integer.