Consider the set that consists of the following six matrices 10 -6) :) I 0 1 C = (3) 0 1 A = D = 1 () :) (3) 1 0 0 1 --(::)) B -1 K = (19)

Find the order of the element 2+ (6) in the group Z30/(6).

Exercise 2.2.6 Consider the affine group AM9) = { (; ")-bez, a#0}. Show that Aff(3) is a group under matrix multiplication as defined in formula (1.3) of Section 1.8 and the statement that follows it. Draw a Cayley graph for this group with { (6 ):6 1)} Compare with the Cayley graph X (Da, {R, F} ) Are generating set S= these groups really the same in some sense (a sense to be known to us as isomorphic groups in Section 3.2)?