WAEC 2016 · Paper 2 · Q1

Binary operations

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

(a)
identity element under the operation $*$ ;
(b)
inverse of $n$ under the operation $*$ .

Worked solution (try it first)

(a)

The identity $e$ satisfies $m * e = m$ : $m + e + 2 = m$ , so $e = -2$ .

(b)

The inverse satisfies $n * n^{-1} = e$ : $n + n^{-1} + 2 = -2$ .
So $n^{-1} = -4 - n$ .

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