# homomorphism :))

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• November 15th 2009, 10:34 PM
GTK X Hunter
homomorphism :))
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! (Rofl)
• November 16th 2009, 01:46 AM
Defunkt
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.