  In this paper, we will prove a matrix weighted $T1$ theorem regarding the
boundedness of certain matrix kernelled CZOs on matrix weighted $L^p(W)$ for
matrix A${}_p$ weights $W$. Using some of the ideas from the proof, we will
also establish a natural matrix weighted John-Nirenberg result that extends to
the matrix setting (in the case when one of the weights is the identity) a very
recent characterization of both S. Bloom's BMO space and the two weight
boundedness of commutators by I. Holmes, M. Lacey, and B. Wick.
