Is the prostration of forgetfulness (sujud al-sahw) obligatory for someone who made a mistake in the wording of the taslim (salutation of peace at the end of prayer), and should they correct the mistake then prostrate?

The key to prayer is purification (tahoor), its beginning is the takbir (Allahu Akbar), and its ending is the taslim (saying Assalamu Alaikum). The majority of scholars hold that a single taslima is sufficient to exit the prayer, while the second taslima is a sunnah. It is sufficient in the taslim to say: "Assalamu Alaikum," and the most complete form is "Assalamu Alaikum wa Rahmatullah." Errors in the taslim are of two types: First, an error that violates the obligation of the taslim, such as omitting it or replacing it with another phrase, which invalidates the prayer if a long time passes or ablution is nullified, requiring its repetition. However, if the worshipper remembers shortly after and before leaving the prayer area, they should perform the taslim and prostrate for forgetfulness (sujud as-sahw). Second, an error that violates the perfection of the taslim, such as omitting the phrase "wa Rahmatullah" or the second taslima. In this case, it is permissible to rectify them and prostrate for forgetfulness.