Every component from the solution of $\dot X = AX, X(t_o)=X_0$ is a non decreasing function in I=[$t_0,oo$]

Question

Let A $\in$ R be a matriz whose elements are non negative. Let $X_0 \in $ R .

Then every component from the solution of $\dot X = AX, X(t_o)=X_0$ is a non decreasing function in I=[$t_0,oo$]

I would like to know if this is really truth, because I am not sure. Any help is greatly appreciated.