I have a newbie question regarding the equality $$W_{ik}=-\omega_l\varepsilon_{ikl},$$
where $\varepsilon_{lik}$ is the Levi-Civita permutation symbol. Now, I want to solve for $\omega_l$ and my question is: Are both of the following two manipulations allowed?
$$(1):-\varepsilon_{ikl}W_{ik}=\omega_l\varepsilon_{ikl}\varepsilon_{ikl}=6\omega_l$$ $$(2):-\varepsilon_{ikq}W_{ik}=\omega_l\varepsilon_{ikl}\varepsilon_{ikq}=2\delta_{lq}\omega_l=2\omega_q$$
In the book i'm using, they chose (2) but I can't find any reason as to why (1) would not be valid, is it simply a matter of taste?
Best regards
Bengt