-(으)ㄹ까요? is for suggestions or wondering - "shall we?" or "do you think?"
Shall we watch a movie together?
Also used for offers (창문 열까요? = Should I open the window?)
Suggestions: 같이 갈까요?
- Shall we go together?
Offers: 도와 드릴까요?
- Should I help you?
Wondering: 비가 올까요?
- Do you think it will rain?
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