Help with Index Notation: εlmn detA = εijkAilAjmAkn

[bothcats]

Homework Statement

Show:
ε_lmn detA = ε_ijkA_ilA_jmA_kn

Homework Equations

not sure

The Attempt at a Solution

I'm really not sure where to begin. I understand index notation (at least I think I do). Can anyone help me get started? I think that once I have the first step, I'll be ok with the rest. Thanks!

 

[Fredrik]

Is the matrix 3×3? What's your definition of det A? If you're using a definition that doesn't look useful, do you know another formula for det A in terms of the components of A, or in terms of the rows or columns of A?