Counting Elements in Hom(V,W) for Finite Linear Transformations

JaysFan31

Homework Statement


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?

Homework Equations


Nothing.

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?
 
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Would the answer still just be n^2?
 

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