GATE EC 2005 Set 1 Q25 — Control Systems

A linear system is equivalently represented by two sets of state equations.
$$\dot{X}=\mathrm{AX}+\mathrm{BU} \text{ and } \dot{W}=\mathrm{CW}+\mathrm{DU} \text{. }$$
The eigenvalues of the representations are also computed as $\{\lambda\}$ and $\{\mu\}$. Which one of the following statements is true?