Answer to Question #15499 in Abstract Algebra for Sujata Roy

Question

Let G = {(a, b) | a, b are real number, b != 0}. Define (a, b) * (c, d) = (a + bc, bd) for all (a, b), (c, d) belongs to G. Then (G, *) is a

a)Commutative group
b)non-commutative group
c)not a group
d)cyclic group.