  We define quantum matrix groups GL(3) by their coaction on appropriate
quantum planes and the requirement that the Poincare series coincides with the
classical one. It is shown that this implies the existence of a Yang-Baxter
operator. Exploiting stronger equations arising at degree four of the algebra,
we classify all quantum matrix groups GL(3). We find 26 classes of solutions,
two of which do not admit a normal ordering. The corresponding R-matrices are
given.
