Can anyone help with the following problem from Dummit and Foote Section 1.4 Matrix Groups.

Show that $\displaystyle GL_n$(F) is a finite group if and only if F has a finite number of elements.

I cannot figure out how to compose & write the proof but suspect that F being finite means a finite number of possible matrices ... hence $\displaystyle GL_n$(F) is finite

Is it as simple as that (in principle anyway)?

Peter