A binary operation * is defined on the set R of all real numbers by the rule for all a, b ∈ R. Write the identity element for * on R.

Question

Philoid · Accepted Answer

The given binary operation is a*b =

We have to find the identity element for the above relation.

Let that element be e.

∴ From the definition of identity element ,

a*e = a

∴ = a

Squaring both sides, we get,

=

∴ e = 0

Thus, the identity element for this operation is 0.