A binary operation ∗ ∗ is defined on a set of real numbers by x ∗ ∗ y = xy for all real values of x and y. If x ∗ ∗ 2 = x. Find the possible values of x

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

Answer Details

x $\ast$ y = xy
x $\ast$ 2 = x2
x $\ast$ 2 = x
∴ x2 - x = 0
x(x - 1) = 0
x = 0 or 1