Math Paper and Grad School Application
If your goal is to have a way to include this in your graduate applications, you can certainly talk about this project in a statement of interest.  Search this site for "statement of interest" and you will see many have no idea what to put there.  You have something concrete to talk about!  Did this experience make you want to study more algebra, or are you ready to switch to analysis?  Do you want to look at applications, or more theory, of matrices over finite fields?

It is a slight disappointment that you did not do this as an independent study, which is what someone my age would have done.  On the other hand, you did get feedback on MathOverflow.  Graduate admissions committees can take into account interactions like this.  I would say this shows independence and a willingness to learn by whatever means available.  You cannot say that in a statement of interest, but you can talk about how you enjoy having Denis Serre answer a question of yours.  (Name-dropping is best done shamelessly.)