A binary operation ⊗ defined on the set of integer...
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?
-5/4
-5/6
zero
5
Correct answer is A
m⊗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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