When you matriculate at your local university, that means that you’ve enrolled there as a student. If you hope to matriculate at a certain school, it means you want to be a student there.
The verb matriculate is often confused the verb graduate — which means a student has completed a course of study. Instead, use matriculate to describe the act of enrolling as a student at a university and save graduate for the day you hurl your tasseled cap at the sky. There is also a noun form of matriculate: a matriculate is someone who has enrolled as a student.