Einstein summation convention proof

[tigger88]

Homework Statement

Using the Einstein summation convention, prove:

A\bulletB\timesC = C\bulletA\timesB

Homework Equations

The Attempt at a Solution

I tried to follow an example from my notes, but I don't entirely understand it. Would it be possible to find out if what I've done (below) is correct, or where I went wrong?

(B\timesC)_{i} = \epsilon_{ijk}B_{j}C_{k}

(A\bulletB\timesC)_{i} = \epsilon_{ijk}A_{i}B_{j}C_{k}

= \epsilon_{kij}A_{i}B_{j}C_{k}

=C\bulletA\timesB

Thanks!
PS. I'm not very familiar with Latex and couldn't get the symbols to line up properly.. sorry! They should all be subscripts.

 

[Dick]

I think that's about right. The thing is just to show that e_{ijk}=e_{jki}, right?