Question

In the set of integers under the operation $\ast$ defined by $a\ast b=a+b-1$, the identity element is:

• A. $0$
• B. $1$
• C. $a$
• D. $b$

Answer 1

Answer: (B)

$1$

Let $e$ be the identity element, then
$\Rightarrow a\ast e=a$
or
$a+e-1=a$
$e-1=0$
$e=1$.
Hence the identity element for the above operation is $1$.