Question

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

• A. $0$
• B. $3$
• C. $4$
• D. $2$

Answer 1

Answer: (A)

$0$

Answer 2

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