Question

If ${}^{\prime }{\ast }^{\prime }$ is a binary operation on the set R of real numbers defined by $a\ast b=a+b-2$, find the identity element for the binary operation ${}^{\prime }{\ast }^{\prime }$.

Answer 1

Given binary operation ${}^{\prime }{\ast }^{\prime }$ is defined as $a\ast b=a+b-2$.

Let e be the identity element of binary operation $\ast$.

Then,

$a\ast e=a+e-2$

$a=a+e-2$

$e=2$