If the binary operation * on the set Z is defined by a*b = a + b – 5, then find the identity element with respect to *.

Question

Philoid · Accepted Answer

Given that binary operation ‘*’ is valid for set ‘Z’ defined by a*b = a + b – 5 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 – 5 = a

⇒ e – 5 = a – a

⇒ e = 5

∴ The required Identity element w.r.t * is 5.