Our dishwasher has saved a lot of 'argh' over the washing of dishes....so now all we have to handwash are pots and cooking utensils and containers, and that doesn't take long so long as I do them every night.
Or if I've cooked something nice, he does them without asking. :-)

So yeah, I think that if A does a 'nice' meal (i.e. it takes a lot of time and effort), then B should offer to do the cleaning after enjoying the food.
If A makes an ordinary meal, then A usually asks B to help with at least stacking the dishwasher. If B is nice, then he will keep going and handwash the rest too. :-)