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

A.

\(-\frac{4}{5}\)

B.

\(-\frac{2}{5}\)

C.

4

D.

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

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

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

\(a^{-1} = -\frac{4}{5}\)