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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
x \(\ast\) y = xy
x \(\ast\) 2 = x2
x \(\ast\) 2 = x
∴ x2 - x = 0
x(x - 1) = 0
x = 0 or 1
Source: Myschool Past Questions Archive (Record #31194)