  In this paper we approach the two weighted boundedness of commutators via
matrix weights. This approach provides both a sufficient and a necessary
condition for the two weighted boundedness of commutators with an arbitrary
linear operator in terms of one matrix weighted norm inequalities for this
operator. Furthermore, using this approach, we surprisingly provide conditions
that almost characterize the two matrix weighted boundedness of commutators
with CZOs and completely arbitrary matrix weights, which is even new in the
fully scalar one weighted setting. Finally, our method allows us to extend the
two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix
weights and a matrix symbol), completing a line of research initiated by the
first two authors.
