On the set Z of integers, if the binary operation * is defined by a*b = a + b + 2, then find the identity element.

Question

Philoid · Accepted Answer

Given that binary operation ‘*’ is valid for set ‘Z’ of integers defined by a*b = a + b for all a,b∈Z.

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

We know that he Identity property is defined as follows:

⇒ a*e = e*a = a

⇒ a + e + 2 = a

⇒ e + 2 = a – a

⇒ e = – 2

∴ The required Identity element w.r.t * is – 2.