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}
\delta_{il} & \delta_{im}& \delta_{in}\\
\delta_{jl} & \delta_{jm}& \delta_{jn}\\
\delta_{kl} & \delta_{km}& \delta_{kn}\\
\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.