$\mathbb{CP}^{2}$ is homeomorphic to $ ( S^2 \times S^2)/\mathbb{Z}_2$

Question

Let $\mathbb{CP}^{n}$ be the set of all complex lines containing origin in $\mathbb{C}^{n+1}$ and $\mathbb{CP}^{n}$ has the quotient topology inherited from the natural projection $\mathbb{C}^{n+1}-\{0\}$ → $\mathbb{CP}^{n}$. How can I show that $\mathbb{CP}^{2}$ is homeomorphic to the orbit space $ ( S^2 \times S^2)/\mathbb{Z}_2$ where $\mathbb{Z}_2$ acts on $ S^2 \times S^2$ defined by $(x,y) \rightarrow (y,x)$, This question was asked in my differential geometry exam and I had no idea about it.