Answer to Question #44352 in Abstract Algebra for Jasvinder Singh

Question

Consider the set of matrices
G = a = 1 0
0 1;b = 0 1
1 0;c = 1 1
0 1;d = 1 0
1 1;e = 1 1
1 0; f = 0 1
1 1
with coefficients in Z2.
a) Make the Cayley table and check that this set forms a group with respect to matrix
multiplication. (You can assume that matrix multiplication is associative.)
b) Find the orders of all the elements in G.
c) Show that the group is isomorphic to S3 by giving an isomorphism f : G -> S3.