(1) Let the set $A=\{x, y, x+y\}, B=\left\{0, x^{2}, x y\right\}$, and $A=B$. Find the values of the real numbers $x$ and $y$.
(3) $\left\{\begin{array}{l}x=1 \\ y=-1\end{array}\right.$ or $\left\{\begin{array}{l}x=-1 \\ y=1\end{array}\right.$