Digital Root always = 9, but why?

Question

n = number of choice

n * 111 = x
x * x = y
The digital root of y = 9

Why is this?

Answer 1

 

y = x * x = (111n)^2 = 12321*n^2

 

Now the digit root of 12321 is 9.

So the digit root of y is always going to be 9 times the digital root of n^2

  which is also a multiple of 9