  Chern-Simons theory on a U(1) bundle over a Riemann surface \Sigma_g of genus
g is dimensionally reduced to BF theory with a mass term, which is equivalent
to the two-dimensional Yang-Mills on \Sigma_g. We show that the former is
inversely obtained from the latter by the extended matrix T-duality developed
in hep-th/0703021. For the case of g=0 (i.e. S^2), the U(1) bundle represents
the lens space S^3/Z_p. We find that in this case both the Chern-Simons theory
and the BF theory with the mass term are realized in a matrix model. We also
construct Wilson loops in the matrix model that correspond to those in the
Chern-Simons theory on S^3.
