Sahih al-Bukhari Book 68, Hadith 13
I asked `Aisha about the option: She said, "The Prophet (ﷺ) gave us the option. Do you think that option was considered as a divorce?" I said, "It matters little to me if I give my wife the option once or a hundred times after she has chosen me."
Allah's Messenger (ﷺ) gave us the option (to remain with him or to be divorced) and we selected Allah and His Apostle . So, giving us that option was not regarded as divorce.
When Ibn 'Umar was asked about person who had given three divorces, he said, "Would that you gave one or two divorces, for the Prophet (ﷺ) ordered me to do so. If you give three divorces then she cannot be lawful for you until she has married another husband (and is divorced by him)."