I'm trying to prove for an n-dimensional vector field that the divergence of the curl of the vector field is zero. I've been toying around with indexing the elements and placing the elements in a matrix but am going round in circles.
The statement I am trying to prove, take $u$ to be an $n$ dimensional vector field,
I want to show :
$\nabla \cdot (\nabla \times u) = 0$