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If $*$ be a binary operation on a set $A$ and $e$ be the identity element w.r.t. *, then $b \in A$ is said to be inverse of $a \in A$ w.r.t. * , if
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$a * b=b * a=e$
$b \in A$ is said to be an inverse of a w.r.t. operation $*$ if $a * b=b * a=e$. [by definition]
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