Given a set of generators of a finite semigroup, a natural way to show that a given element belongs to the semigroup is to provide a product of generators that is equal to this element. The minimum k such that for every set of generators and every element a product of length at most k is enough to prove membership is called the diameter of a semigroup. I will discuss the known bounds for the diameter of finite semigroups of rational matrices, which turn out to be similar to the bounds for transformation semigroups. I will then pose a few questions on how to make the connections between the former and the latter semigroups more precise.