#Unacademy

Question

Find inverse in a*b=a+b-ab for all a,b belongs to Q-{-1}. where Q is a rational number?

please explain how the inverse will satisfy the equation of inverse(a*b=b*a=e)

Answer 1

a/(a-1)

Answer 2

First find the identity element.

$$a \ast e = a $$

$$ a+e-a\cdot e = a \Rightarrow e(1-a) = 0 \Rightarrow e=0$$

Now for inverse

$$a \ast a^{-1} = e $$

$$a + a^{-1} -a\cdot a^{-1} = 0$$

$$a = a\cdot a^{-1} -a^{-1}$$

$$a^{-1}=\frac{a}{a-1}, a\neq 1$$