Prove that $Z_{p^\infty}$ is the injective envelope of $Z_{p}$, could anyone give me a hint for the proof?

We have a set $$M = \{(x,y)\in \mathbb{Z}^2; 0\leq x,y\leq 10\}$$ Let $P$ be a subset of rectangles with vertices in $M$ and with sides parallel to coordinate axis. What is the smallest cardinality of $P$ if we know that we have in $P$ two rectangles $R$ and $R'$ such that $R\subseteq R'$? I k...