A binary operation (ast) is defined on a set of real numbers by x (ast) y = xy for all real values of x and y. If x (ast) 2 = x. Find the possible values of x
-
A.
0, 1 -
B.
1, 2 -
C.
2, 2 -
D.
0, 2
Correct Answer: Option A
Explanation
x (ast) y = xy
x (ast) 2 = x2
x (ast) 2 = x
∴ x2 – x = 0
x(x – 1) = 0
x = 0 or 1