 Reduction modulo a prime in an integral matrix group

For a prime number $p$, reducing every entry modulo $p$ defines a group homomorphism from an integral matrix group to the corresponding matrix group over ${\mathbb{F}}_p$. The target is finite. If an integral matrix $M$ is not the identity, choosing $p$ not to divide one nonzero entry of $M-I$ ensures that its reduction is also nonidentity.