Question

Let * be the binary operation defined on Q. Find which of the following binary operations are commutative

a * b = (a – b)² ∀ a, b ∈ Q

Answer 1

Given that * is a binary operation defined on Q.

a * b = (a – b)², ∀ a, b ∈Q

b * a = (b –a)²

Since, (a – b)² = (b – a)²

Thus, * is commutative.