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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
\(\frac{-5 \times a^{-1}}{2} = 2\)
\(a^{-1} = \frac{2 \times 2}{-5}\)
\(a^{-1} = -\frac{4}{5}\)
Source: Myschool Past Questions Archive (Record #27331)