Question on tensor notation in group theory

[BWV]

in the appendix on Group Theory in Zee's book there is a discussion of commutations for SO(3)

two questions

- does [J^{ij},J^{lk}] = J^{ij}*J^{lk}-J^{lk}*J^{ij}?

and there is an expression in the appendix that the commutator equals i(\delta^{ik}J^{jl} ...

i don't understand the why you are multiplying the matrix by the kronecker delta with different upstairs indexes, is not it simply an identity?

 

[BWV]

bumping this - this apparently is some notation I don't understand, the Wiki entry on Special Unitary groups has this as well

I don't get the significance of the kronecker deltas with the different indexes