1) If V and W are finite dimensional vector spaces over F with

dimension m and n respectively, then prove that Hom(V,W) is also a

finite dimensional vector with dimension mn.

2) If dim V=m, then pt dim Hom(V,V)=m^2

3) If dim V=m, then pt dim Hom(V,F)=m

(Hom --> Homomorphism)

where Hom(V,W)={ T : V --> W, where T is homomorphism }.

Thanks in advance.