Show that $X_1, X_2, X_3$ are pairwise independent but not independent.

Question

Let $X_1,X_2$ be iid RVs with common PMF: $$P(X = \pm1) = \frac{1}{2}$$

We define $X_3 = X_1X_2$. Show that $X_1,X_2,X_3$ are pairwise independent but not independent.

I have shown that these RV's are pairwise independent. How can I prove that these are not independent?