Kronecker delta symmetry?

Question

This is quite a simple question for the Kronecker delta does $$\delta_{ij}=\delta_{ji}$$ My textbook implies it does but does not actually state it and hence am looking for clarification.

Answer 1

This is simple and you are able to prove it on your own.

Write down the definitions on both sides and compare what the result is. Hint: You have to check two different cases.

Answer 2

Note that for general curvilinear coordinates, the property

$$ \delta_{ij} = 0, \: i \neq j \quad \delta_{ij}= 1, \: i=j $$

even if true in one basis, is NOT true in general, because $\delta_{ij}$ transforms as a (0,2) tensor. However, the (mixed) (1,1) Kronecker delta $\delta^i_j$ does have this property.