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: Option A
Explanation
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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