What is the ruling on a man hitting a woman who hit him, and does Allah’s saying apply to him: {Then whoever transgresses against you, transgress against him to the same extent that he transgressed against you}? And is he sinful for his action, or should he have acted differently, and what is the ruling on those who transgressed against him?

The implementation of legal punishments (hudud), retribution (qisas), and discretionary punishments (ta'zirat) falls under the exclusive authority of the ruler. It is not permissible for individual citizens to carry them out without his permission. Whoever does so is in error, because that is an usurpation of the ruler's authority. The man should have referred the matter of the woman who slapped him to the ruler to judge between them. It is not permissible for him to take his right into his own hands, as that leads to chaos and corruption of the societal order.