Data Sufficiency

For all integers n, n*=n(n-1). What is the value of x*?
(1) x*=x
(2) (x-1)*=x-2

answer choices are usual 1,2,3,4,5

My answer is 4 because I find x=2 and x*=2 in both cases
But Kaplan answer is 2, which I am not convinced with.

Please explain if someone can clarify?

Now here if u take statement 1 then its x^2 - x = x
by solving the above equation u will get x = 0, 2
i.e. insufficient.
Now consider statement 2 i.e. (x-1)(x-2)= x-2
if u solve this question, then u will get x^2 - 4x + 4 = 0
=> (x-2)^2 = 0
=> x = 2 and by this u can calculate unique value of x*. i.e. sufficient.
Hence B.

thanks for this .