Don't forget (and not just in LA) that you can only exercise your right to remain silent not by remaining silent, but by saying those words, ideally in response to each individual question.

Otherwise the prosecutor can stand up in court and say you were "uncooperative" and resisted, even obstructed attempts to investigate the crime, and if your lawyer tries to frame this as you exercising your right, the judge will not permit this because you didn't utter the magical incantations.