
homomorphism :))
Suppose $\displaystyle GL(n,\mathbb{R})$ is a multiplicative group of invertible matrix ($\displaystyle n$x$\displaystyle n$). Let $\displaystyle \mathbb{R}$ be an additive group of real numbers. Given $\displaystyle g:GL(n,\mathbb{R})\rightarrow\mathbb{R}$ with $\displaystyle g(A)=tr(A)$.
Is $\displaystyle g$ homomorphism? If yes then prove it! (Rofl)

You should really be able to solve these by yourself!
For g to be a homomorphism, we need that for every $\displaystyle A,B \in GL_n(\mathbb{R}), tr(A)tr(B) = tr(AB)$
I'll leave the rest for you.