Is the prayer of one who is unable to bow and prays sitting on a chair at home valid?

If bowing (ruku') is difficult for you due to unbearable severe pain, then it is permissible for you to pray on a chair, indicating for the bowing from a standing position, or from a sitting position if you cannot indicate for it from standing. The indication (ima') for bowing is done by inclining the head downwards. Prostration (sujud) must be performed if possible; otherwise, you indicate for it, and the indication for prostration should be lower than that for bowing. Mere shyness about praying on a chair in the mosque is not an excuse for missing congregational prayer. The prayers you performed individually are valid, because congregational prayer is not a condition for the validity of the prayer.