1. It is given that is a subgroup of GL2(Q). (a) Show that G= {(6) wit N = = {(6) with a in (+1} and b in in Q} Now let : GS3 be a homomorphism. (c) Show that N < ker(). Hint: () = (1/6)6. (d) Determine the number of possible . with b in b in Q} is a normal subgroup of G and that there is an isomorphism G/N~ (1). Hint: use the first isomorphism theorem. (b) Is it true that N = [G,G]? Hint: compute the commutator of some simple elements of G.