Yes, by definition one option trade for puts or calls with extrinsic value is zero-sum as with no other trades, the final settlement price zeros out the extrins

Yes, by definition one option trade for puts or calls with extrinsic value is zero-sum as with no other trades, the final settlement price zeros out the extrinsic value. Many options trades are done in combination with other products, however, which allows for non-zero sum.