PLEASE EXLAIN ME FASTLY

34) Let z be the set of integers and * be a binary operation of z defined as a * b= a+b-ab for all a,b belonga to z .The inverse of an element a(not equal to 1) belongs to z is

A) a/(a-1) B) a/(1-a) C) (a-1)/a D) none of these

a * b = a + b - ab  { a , b $\in$Z }
Let b be the inverse element of a $\in$ Z - {1}
 Let e be the identity element , then a*b = e

To find the identity element we have a*e = a
So a + e -ae = a
Or e(1-a) = 0
a cannot be 1 , hence e = 0 (1)

So a*b = e
Or a + b  - ab  = 0
Or b(1 - a) = -a
b = -a/(1- a)

Or b = a/(a-1)
 So option A is correct.