Let * be a binary operation on Z defined by a * b = a + b – 4 for all a, b ∈ Z. Find the invertible element in Z.

Answer:

Consider,

a ∈ Z and b ∈ Z be the inverse of a.

a * b = e = b * a

a * b = e and b * a = e

a + b – 4 = 4 and b + a – 4 = 4

b = 8 – a ∈ Z

Hence, 8 – a is the inverse of a ∈ Z