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I'm completely new with the sum notation and Levi-Civita-Symbols. Can somebody tell me if what I did was correct?

Let $a,b \in \mathbb{R}^3$.

I want to prove $$ (b \wedge a) = -(a \wedge b), $$ so I did $$(b \wedge a)_i = \epsilon_{ijk}b_ja_k = - \epsilon_{ikj}b_ja_k = -\epsilon_{ikj}a_kb_j = - (a \wedge b)_i.$$

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    Yes, rotating indices (in three dimensions) preserves the sign. However, in the original post there is no rotation but a simple interchange $ijk \mapsto ikj$, meaning there **is** a flip of sign and hence the proof is valid.2018-05-19

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