Calculate the map $H_2(\mathbb{R} P^2,\mathbb{Z}/2)\to H_2(\mathbb{C} P^2,\mathbb{Z}/2)$ induced by the inclusion $\mathbb{R} P^2\to \mathbb{C} P^2$.
We know that $H_2(\mathbb{R} P^2, \mathbb{Z}/2) \cong H_2(\mathbb{C}P^2, \mathbb{Z}/2) \cong \mathbb{Z}/2$, so there are only two possible maps: trivial and identity.
How one can define which one is induced by inclusion?
