Fundamental System ODE

Question

Let $\epsilon>0$. Look at the ODE \begin{align*} y'(t)=A(t)y(t), \end{align*} with $A\in C(\mathbb R,\mathbb C^{n\times n})$ and $A(t+\epsilon)=A(t), \forall t\in \mathbb R$. Let $Z\in C^1(\mathbb R,\mathbb C^{n\times n})$ be a Fundamental System of the ODE. Show, that there exists a $B$, so that \begin{align*} Z(t+\epsilon)=Z(t)B, t\in \mathbb R \end{align*} Does anyone has a idea, how to solve this task?