JAMB 2000 · UME · Q14

Find the inverse of $p$ under the binary operation $p * q = p + q - pq$ , where $p$ and $q$ are real numbers and zero is the identity.

Worked solution (try it first)

The inverse $q$ of $p$ combines with $p$ to give the identity 0: $p + q - pq = 0$ .
Collect the $q$ terms: $q - pq = -p$ , so $q(1 - p) = -p$ .
Divide by $1 - p$ : $q = \dfrac{-p}{1 - p} = \dfrac{p}{p - 1}$ , option C.