  We obtain the rectifiability of the graph of a bounded variation
homeomorphism $f$ in the plane and relations between gradients of $f$ and its
inverse.
  Further, we show an example of a bounded variation homeomorphism $f$ in the
plane which satisfies the $(N)$ and $(N^{-1})$ properties and strict positivity
of Jacobian of both itself and its inverse, but neither $f$ nor $f^{-1}$ is
Sobolev.
