  In this paper I consider the inverse boundary value problem for a
quasilinear, anisotropic, elliptic equation of the form
$\nabla\cdot(\gamma\nabla u+|\nabla u|^{p-2}\nabla u)=0$, where $\gamma$ is a
smooth, matrix valued, function with a uniform lower bound. I show that
boundary Dirichlet and Neumann data for this equation, in the form of a
Dirichlet-to-Neumann map, determine the coefficient matrix uniquely, in
dimension 3 and higher. This stands in contrast to the classical linear
anisotropic Calder\'on problem where there is a known obstruction to uniqueness
due to the invariance of the boundary data under transformations of the
equation via any boundary fixing diffeomorphism.
