question on group representations

question on group representations

Here is a problem I faced in algebra. $\rho: A_4 \rightarrow End_{\mathbb
C}\mathbb C^{10}$ is a representation of $A_4$. Then there is a vector $v
\in \mathbb C^{10}$ such that $v$ is an eigenvector for all $\rho(g)$, $g
\in A_4$. I think I miss some trick, or something. Any idea will be
appreciated.