A binary operation ⊗ defined on the set of integers is such that m⊗n =…

A binary operation ⊗ defined on the set of integers is such that m⊗n = m + n + mn for all integers m and n. Find the inverse of -5 under this operation, if the identity element is 0

Correct Answer: Option A

Explanation

(m otimes n = m + n + mn)

Let the inverse of -5 be n).

(therefore -5 otimes n = 0)

(-5 + n + (-5n) = 0)

(n – 5n = 5 implies -4n = 5)

(n = -frac{5}{4})