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Math Help - Homomorphism question

  1. #1
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    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> ?
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  2. #2
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    Please put [math ] and [/math ] tags (without the last space) on your LaTex.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    Please put [math ] and [/math ] tags (without the last space) on your LaTex.

    Thanks. I completely forgot to do that. Haha.
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