Question

* be an operation on Z definied by a*b = a + b – ab, ∀ a, b ∈ Z, for any a ∈ Z, a(≠ 1), inverse of a with respect to * is :

(a) a/(a - 1)

(b) a/(1 - a)

(c) (a - 1)/a

(d) 1/a

Answer 1

Answer is (a)

Given, a*b = a + b – ab, ∀ a, b ∈ z

Let a ∈ Z is possible and x is inverse of a, then

According to question

a*x = 0 (∵ 0 is identity)

⇒ a + x – ax = 0

⇒ x(1 – a) = – a