I came to the prayer and said the opening takbir, and then I saw the imam bowing, so I bowed and did not recite al-Fatihah. Does this count as a rak'ah for me?

Question:
He asks and says: If I come to the prayer and the imam has finished reciting the surah, then I say the takbir, and the imam says the takbir to bow, does this count as a rak'ah for me, or is it obligatory for me to make it up because I did not recite al-Fatihah? May Allah reward you with good.

Answer:
In the name of Allah, the Most Gracious, the Most Merciful. Praise be to Allah, Lord of the worlds. May Allah send prayers and blessings upon our Prophet Muhammad, and upon his family and all his Companions. As for what follows, the correct view, which is the position of the majority of the scholars, is that if one comes and the imam is bowing or before bowing, he bows with him, and this rak'ah suffices for him, praise be to Allah, because he has caught it. The evidence for this is that when Abu Bakrah came and the Prophet (peace and blessings be upon him) was bowing, he entered the bowing with him. He bowed before the row, then crept forward and entered the row. When the Prophet (peace and blessings be upon him) finished the prayer, he did not order him to perform the rak'ah in which he caught him. Rather, he said to him, “May Allah increase you in eagerness, and do not do that again,” meaning do not walk while you are in prayer. Because he bowed before the row and then crept until he entered the row, he forbade him from doing that. However, he did not order him to make up the rak'ah, which indicates that it suffices, praise be to Allah. Yes.