It makes us think there is new information or a follow-up question and we spend time opening the thread. Simply click on the Thank button at the bottom left-hand corner of any post you find helpful. I agree with Mike.
Symmetry comes from a Greek word meaning 'to measure together' and is widely used in the study of geometry. Mathematically, symmetry means that one shape becomes exactly like another when you move it in some way: turn, flip or slide.
1. It is defined to be symmetric so that it behaves like a tensor.  --> A tensor does not have to be symmetric. Symmetry may not even be meaningful for, e.g. a two-point tensor (a multilinear map between two separate manifolds) like deformation gradient in continuum mechanics. 2.