Abelianization of a semidirect product by the integers

Let $B\in {\mathrm{GL}}_d(\mathbb{Z})$ and ${\Gamma }_B={\mathbb{Z}}^d{⋊}_B\mathbb{Z}$. If $t$ generates the second factor, then the elements $tn{t}^{-1}{n}^{-1}$ fill $(B-I){\mathbb{Z}}^d$, and henceIf $1$ is not an eigenvalue of $B$, the second summand is finite.