The binary operation * is defined on the set (R) of real numbers by:

Question

a*b=a+b2,a,b,€R.Find the identity element under *

Answer 1

To find the identity element under the binary operation *, we need to find a number e such that for any real number a, a*e = e*a = a.

Let's set a = x (any real number) and find e:

x * e = x + e^2 = x
e^2 = 0
e = 0

Therefore, the identity element under the binary operation * is 0.