Given an invertible matrix $A$ such that all elements in $A$ and in $^{−1}$ are integers, find $|^4|$

Question

I find this question very interesting, but I am having trouble figuring out how to approach the problem.

I know that the $\det(A^{-1}) = 1/\det(A)$, but I'm unsure of where to go from here. If someone can send me in the right direction, it would be very much appreciated.

Thanks in advance, Tommy.

Answer 1

Hint: If $A \in M(n,\mathbb Z)$ is invertible then $\det(A)=\pm 1$.