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.
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 .