A binary operation (ast) is defined on a set of real numbers by x (ast) y = x

^{y}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 = x^{y}

x (ast) 2 = x^{2}

x (ast) 2 = x

∴ x^{2} – x = 0

x(x – 1) = 0

x = 0 or 1