replacement – Symmetry of a point with functions with arguments

Apparently an easy question, but I'm trying to avoid using a direct replacement rule.

As an example, I could take a term like


where this knitted product is symmetrical, and therefore, must evaluate to zero

I am trying to avoid using a replacement rule, since I am trying to generalize.
I tried to use Firm Y Order to try to automatically change the last term by canonical arrangement, but without success.

Any suggestions would be welcome!

I think I'll extend my question to get the exact answer I'm looking for. I'm using a recursion relationship to generate a load of terms, which involve these point products.

Basically, I want to express any point product that has a signature of -1 of canonical order as inverted order, to give rise to some nice cancellations:

For any choice of I jI'm looking for something like:

Yes[Signature[p[i_].P[j_]]== - 1, Return[P[p[pag[p[j].P[i]]]

Can this be easily achieved?

I think the answer is in ConditionalReplacement. Let me try to entangle you.