Question

If $\ast$ is a binary operation on the set R of real numebrs defined by $a\ast b=a+b-2$, then find the identity element for the binary operation $\ast$.

Answer 1

Let e be the identity element. Then $a\ast e=a=e\ast a$.
So, $a\ast e=a\Rightarrow a+e-2=a\therefore e=2$