It's been a long while, but maybe I can give a small push. Take this with a grain of salt

We know that

If then all .

A basis for the space of all nxn matricies, then, is the set of all matricies with 1 as an ij-th entry **, and all the rest being 0. go through all the possibilities.

ex. for a 2x2 matrix, the basis would be

and

EDIT:// ** with