Question 19

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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: 

$\begin{align}  & p*{{p}^{-1}}=e \\ & \text{where }{{p}^{-1}}\text{ is inverse, }e\text{ is the identity element} \\ & p*{{p}^{-1}}=e \\ & p*{{p}^{-1}}=p+{{p}^{-1}}-p{{p}^{-1}}=0 \\ & p=p{{p}^{-1}}-{{p}^{-1}} \\ & p={{p}^{-1}}(p-1) \\ & {{p}^{-1}}=\frac{p}{p-1} \\\end{align}$

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