Determinant of product of matrices

[LagrangeEuler]

Do you know where can I find proven identity
$$det(AB)=det(A)det(B)$$
using Levi Civita symbol.

 

[micromass]

You can find a proof in "Linear Algebra" by Lang. He doesn't exactly use the Levi-Civita symbol, but he rathers works with signs of permutations. But this is of course almost the same as the Levi-Civita symbol, so it should be very easy to rewrite the proof.