Relation between Levi-civita and Kronecker- delta symbol

[Pushoam]

Homework Statement

definition of ε_ijk
ε_ijk=+1 if ijk = (123, 231, 312)
ε_ijk = −1if ijk = (213, 321, 132) , (1.1.1)
ε_ijk= 0,otherwise .
That is,ε_ijk is nonzero only when all three indices are different.

From the definition in Eq. (1.1.1), show that
ε_ijkε_inm= δ_jnδ_km − δ_jmδ_kn , (1.1.4)
where of course there is an implied sum over the i index in Eq. (1.1.4), but the indices j, k, n,and m are free.

Homework Equations

The Attempt at a Solution

By using definition of ε_ijk; I can show that under the values which i,j,k,n,m can take, L.H.S.=R.H.S.

But is there any other better way to show it?
Is there a way such that one will start from L.H.S. and reach to R.H.S.?

 

[Orodruin]

We do not have access to your book so we cannot tell how Eq. (1.1.1) defines the Levi-Civita symbol.

 

[Pushoam]

We do not have access to your book so we cannot tell how Eq. (1.1.1) defines the Levi-Civita symbol.

I have written the definition.