Should a worshiper perform the two prostrations of forgetfulness (Sajdat As-Sahw) if he makes a mistake while performing them, and does his prayer become invalid if he says the Tasleem while in that state?

If a person is certain of having made a mistake (sahw) but doubts whether they performed the prostration of forgetfulness (sujud as-sahw) for it or not, then they should perform it, because the default assumption is that it was not performed. And if they doubt whether they performed one prostration or two for the prostration of forgetfulness, they should perform another. They should not, however, perform another prostration for forgetfulness for their forgetfulness in the prostration of forgetfulness itself, lest the matter become an endless chain. Their prayer is not invalidated by this.