Mark the correct alternative in each of the following:
On Z an operation * is defined by a * b = a2 + b2 for all a, b ∈ Z. The operation * on Z is
1) Commutative:
⇒ a * b = a2 + b2 …(1)
⇒ b * a = b2 + a2 …(2)
⇒ a * b= b * a
2) NOT Associative:
⇒ (a * b)* c = (a2 + b2) * c
= (a2 + b2)2 + c2
⇒ a * (b * c) = a * (b2 + a2)
= a2 + (b2 + c2)2
⇒ (a * b)* c ≠ a * (b * c)