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Consider this group of six matrices:
Let G = <{I, A,B,C,D,K}, Matrix Multiplication>
I = A = B =
C = D = K =
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*, > by y f(x) = det(x) for any Matrix x G.
Question:
By which theorem in linear algebra, is f a Homomorphism from G to <R*, > ?