Question

The identity element for the binary operation * defined on Q ~ {0} as a * b = ab/2 ∀ a, b ∈ Q ~ {0} is 

(A) 1 (B) 0 (C) 2 (D) none of these

Answer 1

(C) 2

Given that, a * b = ab/2 ∀ a, b ∈ Q ~ {0}

Let e be the identity element for * such that

a*e = e*a = a

Now, a * e = ae/2

a = ae/2

⇒ 2a = ae

⇒ e = 2