If $x^2=x$, then $x=1$. Is this statement true or false?

I understand that this equation has two solutions, that is $x=1$ or $x=0$. But if you say this statement is false, you are like saying that $x=1$ is not the solution for the equation. If a basket contains $2$ apples and $1$ orange, and I say that the basket contains $2$ apples. Is there anything wrong? Anyone have a good argument one way or the other?

"$x = 1$" is not at all the same as "$x$ can be $1$". The former states in no uncertain terms that $x$ can only be $1$ and nothing else, but that is not true if you are just given "$x^2 = x$".

It's false. We are not given enough information from $x^2=x$ to deduce that $x=1$.

It's better to look at the contraposition.

Think about it: if $x \neq 1$, does it necessarily follow that $x^2 \neq x$? Can't you find another number which satisfies the equation?