Hello ppl,

Well... I solved it anyway. But I am still open to comments >_<

Proof of

Now consider the subspace of scalar matrices W. We can easily see that . Thus W is non zero G-invariant subspace of Hom(V,V). But data says Hom(V,V) is irreducible and thus W = Hom(V,V). But W is clearly 1 dimensional ( is a basis)