Hadith: The Messenger of Allah (may Allah's peace and blessings be upon him) prayed in his house during his illness

عن عائشة رضي الله عنها قالت: صلى رسول الله صلى الله عليه وسلم في بيته وهو شَاكٍ، صلى جالسا، وصلى وراءه قوم قِيَامًا، فأشار إليهم: أنِ اجْلِسُوا، لما انْصَرَفَ قال: إنما جُعِلَ الإمامُ لِيُؤْتَمَّ به: فإذا ركع فاركعوا، وإذا رفع فارفعوا، وإذا قال: سمع الله لمن حمده فقولوا: ربنا لك الحمد، وإذا صلى جالسا فصلوا جلوسا أجمعون».
[صحيح] - [متفق عليه]

‘Ā'ishah (may Allah be pleased with her) reported that the Messenger of Allah (may Allah's peace and blessings be upon him) prayed in his house during his illness. He prayed while sitting and the people prayed behind him while standing. He pointed to them to sit down. When he had finished the prayer, he said: "Verily, the Imām is appointed in order to be followed. So when he bows, you should bow, and when he raises his head, you should do the same. And if he says: 'Allah hears the one who praises Him,' you should say: 'Our Lord, all praise is due to You.' And if the Imām prays while sitting, you all should pray while sitting as well."
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

This Hadīth contains a description of how the Prophet (may Allah's peace and blessings be upon him) prayed during his illness. It also explains how the congregation should follow the Imām and imitate him. The Prophet (may Allah's peace and blessings be upon him) guided the congregation to the wisdom behind appointing the Imām, which is that he should be followed and imitated in order for people to not act differently from his actions during the prayer. Rather, the movements of the Imām are to be followed in the same order. So if the Imām says the Takbīr of Ihrām, then all of the congregation should do this after him, and if he goes into the bowing position, then all of the congregation should bow after him as well. If the Imām reminds you that Allah answers those who praise Him by saying: "Allah hears the one who praises Him," then you should all praise him by saying: "Our Lord, all praise is due to You". Then when he prostrates, all of you should follow him in prostration, and if the Imām prays while sitting because of his inability to stand, then to manifest complete imitation, you should all pray while sitting, even if you are all able to stand. ‘Ā'ishah (may Allah be pleased with her) mentioned that the Prophet (may Allah's peace and blessings be upon him) felt ill, and he prayed while sitting down for that reason. The companions thought that they should stand up because they had the ability to stand, so they prayed while standing behind him. But the Prophet (may Allah's peace and blessings be upon him) pointed to them that they should sit down. After the Prophet (may Allah's peace and blessings be upon him) finished the prayer, he informed them that people should not act contrary to the Imām and that he should be followed in order to manifest complete imitation and perfect emulation. The congregation should pray while sitting down, even if they have the ability to stand, because their Imām is sitting down due to his inability to stand. If the Imām starts the prayer with them while sitting, then they should all sit, acting upon this Hadīth. However, if the Imām starts the prayer while standing and then becomes sick or ill during the prayer and needs to sit down, then it become obligatory for the congregation to complete the prayer while standing. This is proven by the Hadīth which describes the prayer where the Prophet (may Allah's peace and blessings be upon him) led Abu Bakr and the people when he was experiencing his final illness.