We prove that for any n ≥ 1 there exist n × n matrices A and B such that for any vector x ∈ R with a nonzero first component, the orbit of x under the action of the semigroup generated by A and B is dense in R. As a corollary, we prove that for a large set of diagonal matrices A and B and any vector V with nonzero entries, the orbit of any vector under the semigroup generated by the affine maps...