Let $A_{ab}$ be an antisymmetric vector field, show that $A_{[ab,c]}$ is a tensor.
I tried tackling the problem by showing that $A_{[ab,c]}$= $\frac{1}{3}(A[ab,c]+A[bc,a]+A[ca,b])$.
But from here I can’t seem to figure out how to prove that the previous expression is a tensor since the partial derivatives are not tensors, so maybe someone could direct me the in right way of how to continue from here.
Any help would be appreciated.