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.
- 2/3
- 1/2
- -1/2
-
-2/3
The correct answer is: D
Explanation
\(a*a^{-1} = aa^{-1} + a + a^{-1} = e\)
if e = 0
\(2.2^{-1} + 2 + 2^{-1} = 0\)
collecting like terms, we have:
\(3.2^{-1} + 2 = 0\)
= \(2^{-1}\) = -\(\frac{2}{3}\)