My question is from T.Y.Lam- A First Course in Noncommutative Rings.
For a ring $R$, if all left $R$-modules are semisimple, then all short exact sequences of left $R$-modules split.
A module $M$ is a semisimple module if every submodule $N$ of $M$ is a direct summand, that is there exists a submodule $N'$ such that $M=N \oplus N'$.
In order to prove the proposition above, let $M$ be a left $R$-module and let us consider $0 \rightarrow A \hookrightarrow B \rightarrow C \rightarrow0$ be a short exact sequence, where $A,B$ and $C$ are semisimple left $R$-modules. What should my strategy be in order to $B\cong A \oplus C$.