Question

2. (a) Let a binary operation * on G defined by (a,b)* (c,d) = (ac,bc+d) (i) Show that (G,*) is non-abelian group (ii) If His Subset of G of the form (1,b). Is form Sub group of G. (b) Prove that G(+ , X7 ) is a Filed​

Answer 1

Answer:

Let G={(a,b) | a,b∈R,a≠0}. Let ∗ be an operation on G defined by

(a,b)∗(c,d)=(ac,bc+d)

Prove G is a group.

Is this a group or not? because the commutative property does not hold:

(a,b)∗(c,d)=(ac,bc+d) but (c,d)∗(a,b)=(ca,da+b)