If $J_i$ represent the angular momentum operators, then a scalar operator $S$ (rank-0 tensor) is defined as an operator which satisfies $$[S,J_i]=0$$ for $i=1,2,3$.

$A_i$ is a vector (rank-1 tensor) operator, if it satisfies $$[J_i,A_j]=i\hbar\epsilon_{ijk}A_k$$

How does a rank-2 tensor operator defined in terms of commutators?