  We study the anisotropic Bianchi I loop quantum cosmology in 2+1 dimensions.
Both the $\mubar$ and $\mubar'$ schemes are considered in the present paper and
the following expected results are established: (i) the massless scalar field
again play the role of emergent time variables and serves as an internal clock;
(ii) By imposing the fundamental discreteness of length operator, the total
Hamiltonian constraint is obtained and gives rise the evolution as a difference
equation; and (iii) the exact solutions of Friedmann equation are constructed
rigorously for both classical and effective level. The investigation extends
the domain of validity of loop quantum cosmology to beyond the four dimensions.
