# Thread: Homomorphism question

1. ## Homomorphism question

Consider this group of six matrices:

Let G = <{I, A,B,C,D,K}, Matrix Multiplication>

I = $\left(\begin{array}{cc}1&0\\0&1\end{array}\right)$ A = $\left(\begin{array}{cc}0&1\\1&0\end{array}\right)$ B = $\left(\begin{array}{cc}0&1\\-1&-1\end{array}\right)$

C = $\left(\begin{array}{cc}-1&-1\\0&1\end{array}\right)$ D = $\left(\begin{array}{cc}-1&-1\\1&0\end{array}\right)$ K = $\left(\begin{array}{cc}1&0\\-1&-1\end{array}\right)$

Operation Table for this group:

_|I A B C D K
I |I A B C D K
A|A I C B K D
B|B K D A I C
C|C D K I A B
D|D C I K B A
K|K B A D C I

Define f: G -> <R*, $\bullet$> by y f(x) = det(x) for any Matrix x $/in$ G.

Question:

By which theorem in linear algebra, is f a Homomorphism from G to <R*, $\bullet$> ?

2. Please put [math ] and [/math ] tags (without the last space) on your LaTex.

3. Originally Posted by HallsofIvy
Please put [math ] and [/math ] tags (without the last space) on your LaTex.

Thanks. I completely forgot to do that. Haha.