K=PD[X[1,4,2,5],X[3,6,4,1],X[5,2,6,3]]

SetAttributes[δ,Orderless];
Expand[
Times@@K /. X[i_,j_,k_,l_] :> A δ[i,j]δ[k,l]-(A^(-1))δ[i,l]δ[j,k]
] //. δ[i_,j_]δ[j_,k_] :> δ[i,k] /. δ[i_,i_]|((δ[__])^2):>(-(A^2)-(A^(-2)))

% // Simplify

δ[7,5]