〜ましょう is the polite volitional form, used to suggest doing something together or to offer help.
Invitation/suggestion - "Let's do X together"
Offering help - "Shall I do X for you?"
Let''s eat together.
Add か to make it a question: 行きましょうか？ (Shall we go? / Shall I go?)
Formation from ます-stem
- 食べます → 食べましょう
- 行きます → 行きましょう
- します → しましょう
ましょうか asks for agreement or offers help — context determines meaning
Let's begin!
Shall I open the window?
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