Question

Let be a binary operation on Z defined by a b = a + b – 15 for a, b ∈ Z. The identity element in (Z, *) is

(A) 5

(B) 10

(C) 15

(D) 0

Answer 1

Correct Option :- (C) 15

Explanation :-

Let e be the identity element.

∴ For a ∈ Z, a e = a = e a

⇒ a + e – 15 = a = e + a – 15

⇒ e – 15 = 0 ⇒ e = 15 ∈ Z

∴ The identity element is 15.