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**1. 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

_{ijk}ε

_{inm}= δ

_{jn}δ

_{km}− δ

_{jm}δ

_{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.

**2. Homework Equations**

**3. 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.?

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