Show that every finite simple group G has a faithful irreducible representation A representation $ \rho $ : G  $ \rightarrow $ GL(V) is faithful if ker($ \rho $)={$ e $}. 
A representation is irreducible if it contains no proper invariant subspaces
G is a simple group its normal subgroups are {$ e $} and itself. 
Is there anything that can link these together to prove the above statement? 

Exercise: let $G$ be a simple group and fix a field $K$. Then every nontrivial linear representation of minimal dimension is faithful and irreducible unless $G$ is cyclic of order $p$ and $p=0$ in $K$. In particular, if the simple group $G$ admits a nontrivial linear representation over $K$ (e.g., $G$ is finite), then it admits a faithful irreducible representation (with the same unique exception in char. $p$)
