Find a group such that $x^2 = x$ for all $x$ I have a group $G$ satisfying that $x^2 = x$ for all $x\in G$. I have to find the group. I was thinking that since I am asked to find the group it was probably the trivial group.
My thinking is that since $x^2 = x$ for all $x$, then $x^2x^{-1} = xx^{-1} = 1$. So $x = 1$. So the group is the trivial group. Is that right?
This is homework, so if I am wrong, then please just give me a hint.

Yes you are correct. 
Let $x$ be any element in $G$. $$\begin{align} x^2 = x& \iff x^2x^{-1} = xx^{-1} \\&\iff (xx)x^{-1} = e \\  &\iff= x(xx^{-1})= e \\  &\iff  x = e\end{align}$$ where $e$ is the identity of the group. 
So indeed, since $x$ was chosen arbitrarily, $G$ must be the trivial group.
