Question

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

a * b = a + ab ∀ a, b ∈ Q

Answer 1

Given that * is a binary operation defined on Q.

a * b = a + ab

b * a = b + ab

So clearly, a + ab ≠ b + ab

Thus, * is not commutative.