Levi-Civita symbol and Kronecker delta

[typhoonss821]

Hello everyone, I am stuck when I study Levi-Civita symbol.
The question is how to prove

\varepsilon_{ijk}\varepsilon_{lmn} = \det \begin{bmatrix}<br /> \delta_{il} &amp; \delta_{im}&amp; \delta_{in}\\<br /> \delta_{jl} &amp; \delta_{jm}&amp; \delta_{jn}\\<br /> \delta_{kl} &amp; \delta_{km}&amp; \delta_{kn}\\<br /> \end{bmatrix}

where \varepsilon_{ijk} represents Levi-Civita symbol and \delta_{il} represents kronecker symbol.

Thank you very much^^

 

[slider142]

Have you already established the identity \epsilon_{ijk}\epsilon_{ilm} = \delta_{jl}\delta_{km}-\delta_{jm}\delta_{kl}?

 

[typhoonss821]

Yes I have, but I don't know how to relate it to determinant...

 

[Landau]

Well, you could just write out that determinant and see what happens.