In an solution to a problem I was attempting it uses the fact that,
$$\epsilon_{ijk}\delta_{ij} = 0$$ The explanation I am given says: "the levi-civita is antisymmetric under swaps of i and j whilst the kronecker delta is symmetric under swaps of i and j".
I understand what that means but I am struggling to use that fact to prove the statement above.
Oh nevermind I've figured it out. $$\delta_{ij}\epsilon_{ijk} = -\delta_{ij}\epsilon_{jik}=-\delta_{ji}\epsilon_{jik}=-\delta_{ij}\epsilon_{ijk} \\ \therefore \delta_{ij}\epsilon_{ijk} = -\delta_{ij}\epsilon_{ijk} = 0$$