I need a reference for the following statement:

Let G be a linear algebraic group over algebraically closed field k. Let V be a finite dimensional G-module. The V is sub representation of k[G]^n for some n where k[G] is coordinate ring of G.

I could trace this statement in Steinberg's lecture notes on "Conjugacy Classes in Algebraic groups" but am not happy with the proof there.

Thanks in advance.