Jambmaths question:
Find the inverse of P under the binary operation defined by $p*q=p+q-pq$where p and q are real numbers and zero is the identity
Option A:
p
Option B:
p – 1
Option C:
$\frac{p}{p-1}$
Option D:
$\frac{p}{p+1}$
Jamb Maths Solution:
$\begin{align} & p*{{p}^{-1}}=e \\ & \text{where }{{p}^{-1}}\text{ is inverse, }e\text{ is the identity element} \\ & p*{{p}^{-1}}=e \\ & p*{{p}^{-1}}=p+{{p}^{-1}}-p{{p}^{-1}}=0 \\ & p=p{{p}^{-1}}-{{p}^{-1}} \\ & p={{p}^{-1}}(p-1) \\ & {{p}^{-1}}=\frac{p}{p-1} \\\end{align}$
Jamb Maths Topic:
Year of Exam: