First: the hadith of Ibn Umar. When the news reached the Prophet, he said: “Tell him to take her back.” Taking a wife back can only be consequent upon a divorce having taken effect, for there can be no taking back except after divorce. Thus, the divorce must have taken effect.
Second: the Prophet said, “Tell him to take her back.” Had the pronouncement of divorce not taken effect, he would have said that it had not taken effect. This would have been more appropriate than telling him, “Tell him to take her back,” because if it had not taken effect, then whether he took her back or not, the divorce would be incomplete. Thus, there would be no need to oblige him and say, “Take her back”; rather, he should have said, “Inform him that his divorce has not taken effect.”
Third: one wording of the hadith in Sahih al-Bukhari states: “It was counted as one of his divorces” (1). This is an explicit text establishing that the divorce took effect. The point is that, had it not taken effect, it could not have been counted as a divorce; its being counted as a divorce is evidence that it took effect.
Fourth: the general import of Allah’s saying, “Divorce may be pronounced twice” [al-Baqarah 2:229]. Allah, glorified and exalted is He, did not distinguish whether it occurred during menstruation, during a period of purity in which he had intercourse with her, or otherwise. Thus, Allah, exalted is He, affirmed that divorce takes effect and that the number of times he may take her back is twice. If he divorces her for the third time, she is not lawful for him thereafter until she marries another husband.
This is the position of the four imams—Abu Hanifah, Malik, al-Shafi‘i, and Ahmad ibn Hanbal—and it is the view held by the majority of the ummah.