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Q.
On $Q - \{1\}$ such that $a * b = a + b-ab$. Find the identity element.
Relations and Functions - Part 2
Solution:
Given binary operation is $a * b = a + b-ab$
Let $e$ be an identity element.
Then, for all $a \in Q - \{1\}$, $a * e = a$
$\Rightarrow a+e-ae=a$
$\Rightarrow e\left(1-a\right) = 0$
$\Rightarrow e=0 \in Q-\left\{1\right\}$