Given that * is a binary operation on Z defined by a*b = 3a + 7b for all a,b∈Z.

We know that commutative property is p*q = q*p, where * is a binary operation.

Let’s check the commutativity of given binary operation:

⇒ a*b = 3a + 7b

⇒ b*a = 3b + 7a

⇒ b*a≠a*b

∴ Commutative property doesn’t holds for given binary operation ‘*’ on ‘Z’.