# In the set of integers under the operation $^\ast$ defined by $a^{\ast}b=a+b-1$ the identity element is

$\begin{array}{1 1}(1)0&(2)1\\(3)a&(4)b\end{array}$

Let a be any element and e be the identity element.
Then, $a *e =e * a=a$
$a *e=a$
$a+e-1=a$
$e-1=0$
$e=1$
Hence 2 is the correct answer.