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!