homomorphism :))

**GTK X Hunter** · November 15th 2009, 09:34 PM

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

**Defunkt** · November 16th 2009, 12:46 AM

You should really be able to solve these by yourself!

For g to be a homomorphism, we need that for every $A,B \in GL_n(\mathbb{R}), tr(A)tr(B) = tr(AB)$

I'll leave the rest for you.

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