Mark the correct alternative in each of the following:
Let * be a binary operation on R defined by a * b = ab + 1. Then, * is
1) Commutative:
⇒ a * b = ab + 1 …(1)
⇒ b * a = ba + 1 …(2)
⇒ a * b= b * a
2) NOT Associative:
⇒ (a * b)* c = (ab + 1) * c
(ab + 1) * c = (ab + 1)c + 1
(ab + 1) * c = abc + c + 1
⇒ a * (b * c) = a * (bc + 1)
a * (bc + 1) = a(bc + 1) + 1
a * (bc + 1) = abc + a
⇒ (a * b)* c ≠ a * (b * c)