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

$-\frac{4}{5}$

$-\frac{2}{5}$

Correct answer is A

m * n = $\frac{mn}{2}$

Identify, e = 2

Let a $\in$ R, then

a * a $^{-1}$ = e

a * a $^{-1}$ = 2

-5 * a $^{-1}$ = 2

$\frac{-5 \times a^{-1}}{2} = 2$

$a^{-1} = \frac{2 \times 2}{-5}$

$a^{-1} = -\frac{4}{5}$

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