1. The problem statement, all variables and given/known data The set Hom(V,W) is the collection of all linear transformations from the F-space V to the F-space W. Suppose that F,V, and W are all finite. Suppose that F=Zp for some prime p, that V is n-dimensional over F, and W is n-dimensional over F. How many elements does Hom(V,W) have? 2. Relevant equations Nothing. 3. The attempt at a solution I'm pretty sure it's p^n. I have the proof of dimV=m and dimU=n meaning dimHom(V,U)=mn. How do I transform this proof to the one I want?