Irreducible modules

Suppose $R$ is a commutative ring. A nonzero $R$ -module $M$ is called irreducible if it has no nonzero proper submodules.

Prove that an $R$ -module $M$ is irreducible if and only if $M$ is isomorphic (as an $R$ -module) to $R / I$ for some maximal ideal $I$ of $R$ .
Prove that if $M_{1}$ and $M_{2}$ are irreducible $R$ -modules, then every nonzero $R$ -module morphisms from $M_{1}$ to $M_{2}$ is an isomorphism.
Prove that if $M$ is an irreducible $R$ -module, then the endomorphism ring ${End}_{R} (M)$ is a division ring.

Hints

Consider using some of the Isomorphism Theorems for modules. Also recall the correspondence between submodules and ideals.
The kernel and image of a module morphism are submodules ...
Use the previous part.