Okay. Here's the situation. A1 gets a T for hanging on the rim. After the T is reported, but before the free throws are administered, B1 gets stuck for b!tching to the ref. Are these offsetting?

With out having my rule book with me I would say no. The reason being they were for two separate events.

There are no offsetting penalties in basketball. There are penalties where you would go to the AP arrow. The situation you described is not one of them. You enforce the penalties in the order they occurred. This is also assuming you are talking NF rules.

Peace

A double T is carries only the AP possession. Whether they officially call it "offsetting" is of little concern to me. The fact is, they would offset each other. We ended up not shooting and going AP here.
Adult men's league, I'm not overly concerned about not shooting 4 free throws; but wanted to know how to do it in a hs game next season if it ever comes up. My P was the R here, and he wanted to offset them. I just wanted this game to end, so I wasn't overly anal about it.

"Offsetting" is a term used in the game of football. When penalties offset, you replay the down or have a do-over. There is no such animal in basketball. You have to shoot every foul unless it is a double foul. It is that simple. Since this was a Men's league, I really would not care how I applied the rule.

Peace

"Offsetting" is also a term used in basketball. Have a look at 10-4-4 penalty.

Casebook plays 10.4.4SitC says "Because the substitute's fouls were <b>offsetting</b>, no free throws will be awarded.

Casebook play 10.4.4SitD also says "The free throws for one substitute's foul by each team are cancelled as the penalties <b>offset</b>."