Thread: I have a question about eigenstates of an operator.

So I have an operator X, which acts on a state.

I was wondering what I can conclude about the state if it is an eigenstate of X^2 and not eigenstate of X.

So far.. I think is that there is no such state, but I have no clear explanation

It will have a definite value of x^2, (say 9), but not x, (say it could be +3 or -3).