Does the prayer of one who forgot the opening supplication, then remembered it after reciting Al-Fatiha and returned to recite it, become invalidated?

If a worshipper omits a wajib (necessary act) or a sunnah (recommended act) in prayer and begins the next pillar, he should not return to it. So, if he starts reciting Surah Al-Fatiha, he should not go back to recite the opening supplication (Du'a al-Istiftah). Even if he were to return, his prayer would not be invalidated. Permissible verbal acts in prayer do not invalidate the prayer by repetition or by performing them in the wrong place, except for the taslim (salutation of peace). This is in contrast to adding an extra physical pillar, which does invalidate the prayer.