What is the legal ruling on reciting "Iyyaka na'budu" (إياك نعبده) instead of "Iyyaka na'budu" (إياك نعبد) in Al-Fatiha during prayer, and does this invalidate the prayer?

Al-Fatihah is one of the pillars of prayer, and great care must be taken in memorizing and reciting it. If one omits a letter or a shaddah (doubling sign) from it, their prayer is invalid, because a shaddah is equivalent to a letter. As for adding a letter, this is a forbidden error if the person is knowledgeable and capable of learning. However, the prayer is not invalidated unless it changes the meaning and is done intentionally.

Adding "na'buduhu" (we worship Him) after "Iyyaka na'budu" (You alone we worship) does not change the meaning, so the prayer is valid. There is no sin upon the ignorant person, but it is obligatory to learn Al-Fatihah and recite it to a teacher to correct the recitation.