JAMB 2012 · UTME · Q22✱✱

Binary operations

A binary operation on the set of real numbers is defined by $m * n = \frac{mn}{2}$ for all $m, n \in \mathbb R$ . If the identity element is 2, find the inverse of $-5$ .

Worked solution (try it first)

The inverse $x$ of $-5$ combines with it to give the identity 2: $-5 * x = 2$ .
Use the rule: $\frac{-5x}{2} = 2$ .
Multiply both sides by 2: $-5x = 4$ .
Divide by $-5$ : $x = -\frac45$ , option A.

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