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 .
Explanation
(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)