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The binary operation on the set of real numbers is defined by m*n = (frac{mn}{2})…

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})

There is an explanation video available below.

Explanation Video

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