Question

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

a * b = a – b ∀ a, b ∈ Q

Answer 1

Given that * is a binary operation defined on Q.

a * b = a – b, ∀ a, b ∈ Q and b * a = b – a

So, a * b ≠ b * a

Thus, * is not commutative.