I am trying to understand tensor notation for matrix calculations. Is it ok to say, for example, that:
$\epsilon_{ijk}a_{jq}a_{kr}a_{ip} = \epsilon_{ijk}a_{ip}a_{jq}a_{kr}$?
We know that $\epsilon_{pqr}|A|=\epsilon_{ijk}a_{ip}a_{jq}a_{kr}$, and $\epsilon_{ijk}$ is the well-known "Levi-Civita tensor". So essentially, what I am asking is if you can switch the columns and still having the determinant equal? I think the answer is that as long as the permutation of $(i,j,k)$ is even, then there is no issue. In other words, the indices are arranged in a cyclical fashion. So if $j \rightarrow k \rightarrow i$, then certainly $i \rightarrow j \rightarrow k$. That is, we can just say that $\epsilon_{ijk}a_{jq}a_{kr}a_{ip} = \epsilon_{ijk}a_{ip}a_{jq}a_{kr}$ because the indices are cyclic.
Is this correct?
Sorry if the question seems too trivial, I am trying to understand tensor notation for myself.