Originally Posted by

**dori1123** If $\displaystyle R$ is a division ring and $\displaystyle V$ is a left vector space over $\displaystyle R$ with $\displaystyle dim(V)=n$, then $\displaystyle End_R(V)$ is isomorphic to $\displaystyle Mat_n(R^{op})$ and $\displaystyle End_R(V)$ is a left semisimple ring.

I already prove the part that $\displaystyle End_R(V)$ is isomorphic to $\displaystyle Mat_n(R^{op})$, and need help proving that $\displaystyle End_R(V)$ is a left semisimple ring. Any help would be appreciated. Thank you.