Examples of a non-abelian group GL(2), 2 by 2 non-singular real matrices under matrix multiplication a b GL(2)= ad-bC=0 if a and b are non-singular so is aB the identity is I=o1] a c al/(ad-bc) matrIx multiplication is associative matrix multiplication is not commutativeExamples of a non-abelian group GL(2), 2 by 2 non-singular real matrices under matrix multiplication • if A and B are non-singular, so is AB • the identity is I = [ ] • = /(ad-bc) • matrix multiplication is associative • matrix multiplication is not commutative GL(2) = {[ ], ad-bc = 0} a b c d 1 0 0 1 [ ] a b c d -1 [ ] d -b -c a