For all integers n, n* = n(n – 1). what is the value of x*

For all integers n, n* = n(n – 1). what is the value of x* when x is an integer?

(1) x* = x

(2) (x – 1)* = x – 2

My questions is whether you are algebraically allowed to divide by X if you have the equation: x(x-1) = x. Dividing by x yields x-1 = 1 whereas not dividing yields x^2 - 2x.

Changes the answer...

Thanks!