On the non--multiplicity of solutions to matrix equations on time scales

In this paper we establish the non--multiplicity of solutions to first order matrix dynamic equations on time scales. The new results verify and extend the notions developed in \cite{thesis} to more complex systems of $n^2$ matrices with the help of ideas developed in \cite[Chap 5]{BP}, identifying Lipschitz conditions suitable to generalised $n^2$--models on time scales.