Let $q$ be an integer, then there is a one to one corrispondence between $\hom_{\mathbb{Z}_q}(\mathbb{Z}_q^m, \mathbb{Z}_q^n)$ (in my case $m > n$) and the matrices $\mathbb{Z}_q^{n \times m}$.
A particular case is when $q$ is a prime and so $\mathbb{Z}_q$ is a field. In this case a morphism - identified with a matrix $A$, is surjective iff all the rows of $A$ are linear independent or equivalently if $\mathrm{rk}(A) = n$.
My question: is it possible to deduce from a matrix if the associated morphism is surjective, in a way similar to the case when $q$ is prime? Every kind of reference is higly appreciated too