To get rid of all the terms containing the 0 ( - Matrix) you should try
Res1 = Res /. 0 -> Null /. Null.x_ -> Null /. x__.Null -> Null /. a_ Null + x_ -> x /. Transpose -> trp; Res1 // MatrixForm
Thanks a lot Hans.
What about doing it yourself?
Res = Table[ Sum[A[[i, my]].P[[my, ny]].A[[k, ny]], {my, 1, 6}, {ny, 1, 6}], {i, 1, 6}, {k, 1, 6}]
