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 .
(i) \(m * n = m + n + 2\)
Let the identity element be e.
Then \(m * e = m + e + 2 = m\)
\(e = -2\)
(ii) Let N be the inverse of n.
Then \(n * N = e\)
\(n * N = n + N + 2 = -2\)
\(n + N = -4 \implies N = -4 - n\)
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