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 $$(b \wedge a)_i = \epsilon_{ijk}b_ja_k = - \epsilon_{ikj}b_ja_k = -\epsilon_{ikj}a_kb_j = - (a \wedge b)_i.$$