Relationship between Kronecker Delta and the Alternating Tensor

In my Vector Calculus class the book discusses the relationship between Kronecker Delta ($\displaystyle \delta_{ij}$) and the alternating tensor ($\displaystyle \epsilon_{ijk}$) as the following:

$\displaystyle \epsilon_{ijk}\epsilon_{klm} = \delta_{il}\delta_{jm} - \delta_{im}\delta_{jl}$

The book gives a lengthy explanation of why these two expressions are equivalent, but gives no insight as to how this relation was derived.

Can anyone give any insight into the derivation of this equation?

Thanks in Advanced,

James Elmore

P.S.

Is this the right board for this topic?