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
Correct Answer: Option 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})