\[\nabla\mathbf{F}^T \to \begin{bmatrix} \partial_xF_x & \partial_xF_y & \partial_xF_z\\ \partial_yF_x & \partial_yF_y & \partial_yF_z \\ \partial_zF_x & \partial_zF_y & \partial_zF_z \end{bmatrix} =\mathbf{J}^T\]
Inverses, \[\nabla^{-1}=\frac{1}{3} \begin{bmatrix} \partial_x^{-1} & \partial_y^{-1} & \partial_z^{-1} & \end{bmatrix}\]
Such that \(\nabla^{-1}\mathbf{B}=\nabla^{-1}(\nabla\phi)=\phi\)...