How to prove determinant for second order tensors? I was asked in an exam to prove the following expression,
$$ \det(A) = \dfrac16 \epsilon_{ijk}\epsilon_{lmn}A_{il}A_{jm}A_{kn}$$
I know that it can be written in the following form,
$$ \det(A) = \epsilon_{ijk}A_{i1}A_{j2}A_{k3}$$
I don't know how to proceed beyond it.

Will someone please help me, Thank you.
Just start with right hand side and expand it. There are 6 dummy indices (i,j,k,l,m,n). So if you expand them as per summation - you will get to the answer.
Just start with right hand side and expand it. There are 6 dummy indices (i,j,k,l,m,n). So if you expand them as per summation - you will get to the answer.