# tensor product, isotropic

Assume that $T_{ijkl}$ is a 4-th rank isotropic tensor. Why is it $\epsilon_{ijk}T_{ijkl}=0$, without assuming the general formula for a 4-th rank isotropic tensor $\alpha \delta_{ij}\delta_{kl}+\beta\delta_{ik}\delta_{jl}+\gamma\delta_{il}\delta_{jk}$?

Just a hint, both $T$ and $\epsilon$ are isotropic tensors. Is their contraction also isotropic?