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*, > ?