  We use the matrix product formalism to find exact ground states of two new
spin-1 quantum chains with nearest neighbor interactions. One of the models,
model I, describes a one-parameter family of quantum chains for which the
ground state can be found exactly. In certain limit of the parameter, the
Hamiltonian turns into the interesting case $H=\sum_i ({\bf S}_i\cdot {\bf
S}_{i+1})^2$. The other model which we label as model II, corresponds to a
family of solvable three-state vertex models on square two dimensional
lattices. The ground state of this model is highly degenerate and the matrix
product states is a generating state of such degenerate states. The simple
structure of the matrix product state allows us to determine the properties of
degenerate states which are otherwise difficult to determine. For both models
we find exact expressions for correlation functions.
