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A binary operation $*$ is defined on the set, $R$, of real numbers by $m * n=m+n+2$. Find the :

(a) identity element under the operation ;
(b) inverse of $n$ under the operation.
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(i) $m * n=m+n+2$
Let the identity element be e.
Then $m * e=m+e+2=m$
$e=-2$
(ii) Let $\mathrm{N}$ be the inverse of $n$.
Then $n * N=e$
$n * N=n+N+2=-2$
$n+N=-4 \Longrightarrow N=-4-n$
by Platinum (131,378 points)

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