Kaplan DS question

[milindss]

Data Sufficiency :
For All integers n, n^*=n(n-1). What is the value of x^* ?

1) x^*=x
2) (x-1)^*=x-2

SPOILER: Official Answer: B

[milindss]

I have a doubt about the Official Answer explanation.
Stmt1 : Can be written as :
x(x-1)=x
so ..
x-1=1
thus x=2
But, the official explanation does not cancel out the x from both side, instead its written as :
x^2-x=x
x^-2x=0
x(x-2)=0
so x =0 or x=2 hence Insuff.

May be this is very stupid of me .. or its just tooo late n I am feeling sleepy.

[amitabh007]

NEVER ...in an equation problem cancel x from both sides...because by doing that u are eliminating a possibility of x=0...which can very much be the value of x in...x(x-1)=x...if u put x=0 on both the sides its still true.............................................. .............NEVER*0

ALWAYS....bring them to any one of the sides and take common............................................ .......................ALWAYS^INFINITY..

[milindss]

Yeah thanks for the feedback. I really appreciate it.