Question

If the binary operation * on the set Z of integers is defined by a * b = a + b – 5, then write the identity element for the operation in Z.

Answer 1

Let e ∈ Z be required identity

∴ a * e = a ∀ a ∈ Z

⇒ a + e – 5 = a

⇒ e = a – a + 5

⇒ e = 5