Cokernel of injective endomorphisms of a finitely generated free abelian group

Question

By $\text{GL}^+(n,\mathbb{Z})$ we mean the set of $n×n$ invertible matrices with positive determinant and entries from $\mathbb{Z}$. For given $A \in \text{GL}^+(n,\mathbb{Z})$ let $F_A=\mathbb{Z}^n/A\mathbb{Z}^n$ denote the cokernel of $A$. I would like to compute $|F_A|$. How does one do this?