A binary operation * is defined by a*b = ab+a+b for any real number a and b. if the identity element is zero, find the inverse of 2 under this operation.
A
2/3
B
1/2
C
-1/2
D
-2/3
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(a*a^{-1} = aa^{-1} + a + a^{-1} = e\)
if e = 0
\(2.2^{-1} + 2 + 2^{-1} = 0\)
collecting like terms, we have:
\(3.2^{-1} + 2 = 0\)
= \(2^{-1}\) = -\(\frac{2}{3}\)
Source: Myschool Past Questions Archive (Record #19)