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The lecture notes states that if ##T_{ij}=T_{ji}## (symmetric tensor) in frame S, then ##T'_{ij}=T'_{ji}## in frame S'. The proof is shown as $$T'_{ij}=l_{ip}l_{jq}T_{pq}=l_{iq}l_{jp}T_{qp}=l_{jp}l_{iq}T_{pq}=T'_{ji}$$ where relabeling of p<->q was used in the second equality. Where I am confused is that after the 3rd equality, the order of ##l_{iq}## and ##l_{jp}## changes. Is this allowed in all tensors?

Thanks in advance

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# Symmetric Tensor invariance

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