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Solve the following.
A binary operation * defined on mathbbQ - {1} is given by a * b = a + b - ab. Find the identity…
A binary operation $*$ defined on $\mathbb{Q} - \{1\}$ is given by $a * b = a + b - ab$. Find the identity element.
Answer
Answer
Let $e$ be the identity: $a * e = a$ for all $a \in \mathbb{Q} - \{1\}$.
$a + e - ae = a$
$e(1 - a) = 0$, and $a \ne 1$, so $e = 0$.
Hence the identity element is $0$.
Final answer: $0$