Find the identity element in the set of all rational numbers except – 1 with respect to * defined by a*b = a + b + ab

Question

Philoid · Accepted Answer

Given that binary operation ‘*’ is valid for set of all rational numbers Q defined by a*b = a + b + ab for all a,b∈R.

Let us assume a∈R and the identity element that we need to compute be e∈R.

We know that he Identity property is defined as follows:

⇒ a*e = e*a = a

⇒ a + e + ea = a

⇒ e + ae = a – a

⇒ e(1 + a) = 0

⇒ e = 0

∴ The required Identity element w.r.t * is 0.