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
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Correct Answer: Option A
Explanation:
m * n = \(\frac{mn}{2}\)
Identify, e = 2
Let a \(\in\) R, then
a *Â a\(^{-1}\) = e
a *Â a\(^{-1}\) = 2
-5 *Â a\(^{-1}\) = 2
\(\frac{-5 \times a^{-1}}{2} = 2\)
\(a^{-1} = \frac{2 \times 2}{-5}\)
\(a^{-1} = -\frac{4}{5}\)
m * n = \(\frac{mn}{2}\)
Identify, e = 2
Let a \(\in\) R, then
a *Â a\(^{-1}\) = e
a *Â a\(^{-1}\) = 2
-5 *Â a\(^{-1}\) = 2
\(\frac{-5 \times a^{-1}}{2} = 2\)
\(a^{-1} = \frac{2 \times 2}{-5}\)
\(a^{-1} = -\frac{4}{5}\)