What is the ruling of Islamic law regarding a man who killed his brother, who had committed the abomination of adultery with his daughter, with the intention of preserving honor, and is this brother considered a sinner who will be punished on the Day of Judgment for his crime?

Adultery is a grave indecency, and if it is committed with a dhāt mahram (unmarriageable kin), the prohibition is even stronger. There is disagreement regarding the authenticity of the hadith: "Whoever commits intercourse with a dhāt mahram, kill him." However, a muḥṣan (married) adulterer is to be killed, even if the act was not with his mahram, if his adultery and iḥṣān (being married) are established by evidence, confession, or pregnancy. Drinking alcohol is a crime, and it does not negate the ḥadd (prescribed punishment) for the adulterer, even if he committed the act under the influence of alcohol. Adultery is established by confession or by the testimony of four upright witnesses. The implementation of ḥudūd (prescribed punishments) is the prerogative of the ruler or his deputy. Therefore, a brother killing his brother is a grave error, and whoever intentionally kills a believer, his recompense is Hell. Informing the killer of the adultery and letting him commit the crime of murder is a mistake. The killer's repentance and surrendering himself to the guardians of the deceased are reasons for the forgiveness of his sin.