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?
A
-5/4
B
-5/6
C
zero
D
5
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(m \otimes n = m + n + mn\)
Let the inverse of -5 be n.
\(\therefore -5 \otimes n = 0\)
\(-5 + n + (-5n) = 0\)
\(n - 5n = 5 \implies -4n = 5\)
\(n = -\frac{5}{4}\)
Source: Myschool Past Questions Archive (Record #9323)