What is the Tensorial Property of Symmetry for Covariant Second Rank Tensors?

[greenclouds]

How can I explain that the fact that a covariant second rank tensor is symmetric in
one coordinate system is a tensorial property. This is for my GR course, but I didn't do a Tensor Calculus before.

 

[fzero]

You might want to start with the equation that describes how such a tensor transforms under a change of coordinates.