Levi-Civita Tensor: Index Interchange Identity

[AxiomOfChoice]

Does the following identity hold?:

$$\epsilon_{ijk} a_j b_k = -\epsilon_{ijk} a_k b_j$$

 

[cristo]

Yes.

 

[confinement]

The answer is yes; clearly we have:
$$\epsilon_{ijk} a_j b_k = -\epsilon_{ikj} a_j b_k$$

from which we can obtain your identity by relabeling the dummy indices j and k.