I saw that whenever Messenger of Allah ﷺ stood for the prayer, he used to raise both his hands up to the shoulders, and used to do the same on saying the Takbir for bowing and on raising his head from it and used to say, "Samiʿa l-lahu liman hamidah". But he did not do that (i.e. raising his hands) in prostrations.  

رَأَيْتُ رَسُولَ اللَّهِ ﷺ إِذَا قَامَ فِي الصَّلاَةِ رَفَعَ يَدَيْهِ حَتَّى يَكُونَا حَذْوَ مَنْكِبَيْهِ وَكَانَ يَفْعَلُ ذَلِكَ حِينَ يُكَبِّرُ لِلرُّكُوعِ وَيَفْعَلُ ذَلِكَ إِذَا رَفَعَ رَأْسَهُ مِنَ الرُّكُوعِ وَيَقُولُ سَمِعَ اللَّهُ لِمَنْ حَمِدَهُ وَلاَ يَفْعَلُ ذَلِكَ فِي السُّجُودِ  

I saw Malik bin Huwairith saying Takbir and raising both his hands (on starting the prayers and raising his hands on bowing and also on raising his head after bowing. Malik bin Huwairith said, "Messenger of Allah ﷺ did the same."  

أَنْ يَرْكَعَ رَفَعَ يَدَيْهِ وَإِذَا رَفَعَ رَأْسَهُ مِنَ الرُّكُوعِ رَفَعَ يَدَيْهِ وَحَدَّثَ أَنَّ رَسُولَ اللَّهِ ﷺ صَنَعَ هَكَذَا