# Help with tensor homework

if $\epsilon_{ijk} P_{kj}=0$ how do we show $P_{ij}=P_{ji}$?

dx
Homework Helper
Gold Member

Expand out the LHS for each i.

do you mean just substitute in numbers and see what happens because that works - i was just wondering if i could do it without explicitly using numbers (i.e. all of it in index notation).

dx
Homework Helper
Gold Member

For i = j, clearly Aij = Aji, so you only need to check the cases in which i ≠ j.

For example, setting i = 1 in εijkAkj = 0, you get ε123A32 + ε132A23 = A32 - A23 = 0 ⇒ A32 = A23.

You just need to do the same with i = 2 and i = 3.