Question 30

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

• (i)a * b = a – b ∀ a, b ∈Q
• (ii)a * b = a2 + b2 ∀ a, b ∈ Q
• (iii)a * b = a + ab ∀ a, b ∈ Q
• (iv)a * b = (a – b)2 ∀ a, b ∈ Q