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?
\(m \otimes n = m + n + mn\)
Let the inverse of -5 be n.
\(\therefore -5 \otimes n = 0\)
\(-5 + n + (-5n) = 0\)
\(n - 5n = 5 \implies -4n = 5\)
\(n = -\frac{5}{4}\)
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