In particular, Cramer's rule can be used to prove that the divergence operator on a Riemannian manifold is invariant with respect to change of coordinates. We give a direct proof, suppressing the role of the Christoffel symbols. Let ( M , g ) {\displaystyle (M,g)} be a Riemannian manifold equipped with local coordinates ( x 1 , x 2 , … , x n ) {\displaystyle (x^{1},x^{2},\dots ,x^{n})} .