Question

Let be a binary operation on Z defined by a b = a + b – 15 for a, b ∈ Z. The inverse of element 21 in (Z, *) is

Answer 1

Let a ∈ Z and b be its inverse

∴ a b = e = b a

⇒ a + b – 15 = 15 = b + a – 15

⇒ b = 30 – a ∈ Z

∴ The inverse of a ∈ Z is 30 – a