Marginal stability with non-simple poles on the imaginary axis It is known that a system marginally stable if and only if the real part of every pole in the system's transfer-function is non-positive, one or more poles have zero real part, and all poles with zero real part are simple roots (i.e. the poles on the imaginary axis are all distinct from one another).[Wikipedia].
My question is based on the definition, a system with state space representation (A,B,C), where 
$A = \begin{bmatrix} 0 & 0\\ 0 & 0 \end{bmatrix}$ that has a non simple root at origin, is considered unstable? why?

Since not all the eigenvalues of $A$ are negative, then your system is not asymptotically stable. However, even having all the eigenvalues on the complex axis you system can be unstable in the sense BIBO (Bounded Input / Bounded Output) but marginally stable (if all the zero eigenvalues are simple). Check the answer from @Rodrigo for more details.
