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

Question

Philoid · Accepted Answer

The given binary operation is a*b =

Let e be the identity element

Thus, as per the definition of an identity element a*e = a

Applying this in the relation given we have

= a

Or, =1

∴ e =

Thus, the identity element for the given binary operation is .