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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