Question 22

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Jambmaths question: 

The binary operation * is defined 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 .

Option A: 

$-\tfrac{4}{5}$

Option B: 

$-\tfrac{2}{5}$

Option C: 

4

Option D: 

5

Jamb Maths Solution: 

$\begin{align}  & m*n=\frac{mn}{2} \\ & \text{Let }{{m}^{-1}}\text{ be inverse of }m \\ & \therefore m*{{m}^{-1}}=e\text{     }\!\!\{\!\!\text{ }e\text{ is the identity element }\!\!\}\!\!\text{ } \\ & 5*{{m}^{-1}}=2 \\ & 5*{{m}^{-1}}=\frac{5\times {{m}^{-1}}}{2}=2 \\ & 5{{m}^{-1}}=4 \\ & {{m}^{-1}}=\tfrac{4}{5} \\\end{align}$

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