Standing, bowing and prostrating are pillars or essential parts of the Prayer. Whoever can do them, it is obligatory for him to do them in the manner prescribed in shari`ah. Whoever is not able to do them because of sickness or old age, it is Sunnah for him to sit on the ground or on a chair.
It was narrated that ‘Imran ibn Husayn (may Allah be pleased with him) said: I had haemorrhoids so I asked the Prophet (peace and blessings be upon him) about praying. He said: “Pray standing up; if you cannot, then pray sitting down; and if you cannot, then pray (lying) on your side.” (Narrated by al-Bukhari)
Al-shawkani said: The hadith of `Imran indicates that it is permissible for one who has an excuse and cannot stand to pray sitting, and for one who has an excuse and cannot pray sitting to pray lying on his side.
Sheikh al-Islam Ibn Taymiyah said: The Muslims are agreed that if a worshipper is unable to do some of the obligatory duties of the Prayer, such as standing, reciting, bowing, prostrating, covering the `awrah, facing the qiblah etc, then what he is unable to do is waived for him
Based on that, if a person offers an obligatory Prayer sitting when he is able to stand, his Prayer is invalid.
It should be noted that if a person is exempted from standing, his excuse does not make it permissible for him to sit on the chair when bowing or prostrating.
If he is exempted from bowing and prostrating in the proper manner, that excuse does not make it permissible for him to neglect standing and to sit on the chair instead.
The basic principle with regard to the obligatory duties of Prayer is that whatever the worshipper can do, he is obliged to do it, and whatever he is unable to do, is waived for him.
Whoever is unable to stand, it is permissible for him to sit on a chair during the standing position, and he should bow and prostrate in the proper manner. If he is able to stand but it is difficult for him to bow and prostrate, he should pray standing, then sit on the chair when bowing and prostrating, and he should bend lower for the prostration than for the bowing.