Do I need to update BRP after changing foreign passport?

[mikewoods]

Hi, to knowledgeable friends, just a simple question:
I'm holding UK BRP and non-UK passport. I'm planning to visit home country to change passport and visit family.
1. Once I get the new passport, do I need to update/change my BRP which was issued upon my application made by the old passport ?
2. Without changing the BRP, can I return to UK by the new passport + BRP?

Thanks very much!