The super approximation property of ${\mathrm{S}\mathrm{L}}_2(\mathbb{Z}\mathrm{/}q\mathbb{Z})\times {\mathrm{S}\mathrm{L}}_2(\mathbb{Z}\mathrm{/}q\mathbb{Z})\times {\mathrm{S}\mathrm{L}}_2(\mathbb{Z}\mathrm{/}q\mathbb{Z})$

Take $S\subset {\mathrm{S}\mathrm{L}}_2(\mathbb{Z})\times {\mathrm{S}\mathrm{L}}_2(\mathbb{Z})\times {\mathrm{S}\mathrm{L}}_2(\mathbb{Z})$ be finite symmetric and assume $S$ generates a group $G$ which is Zariski-dense in ${\mathrm{S}\mathrm{L}}_2\times {\mathrm{S}\mathrm{L}}_2\times {\mathrm{S}\mathrm{L}}_2(\mathbb{Z})$. This paper proves that the Cayley graphs $$\{\mathcal{C}ay(G(q),S(q)){\}}_{q\in {\mathbb{Z}}_{+}}$$ form a family of expanders.