Question

On $Q-\{1\}$ such that $a\ast b=a+b-ab$. Find the identity element.

• A. $0$
• B. $3$
• C. $4$
• D. $2$

Answer 1

Answer: (A)

Given binary operation is $a\ast b=a+b-ab$
Let $e$ be an identity element.
Then, for all $a\in Q-\{1\}$, $a\ast e=a$
$\Rightarrow a+e-ae=a$
$\Rightarrow e\left(1-a\right)=0$
$\Rightarrow e=0\in Q-\left\{1\right\}$