As covered in our
ましょう lesson,
ましょう is one of the conjugations of the auxiliary verb ます, and is a common (polite) way to suggest that something be done ‘together’.
Adding the particle
か to this expression simply changes the nuance from ‘let’s’, to ‘shall we?’, and is more of a direct question than
ましょう by itself.
Like
ましょう, this expression can be added to the ます stem form of any verb.
One thing to note with these examples is that they are ‘suggestions’, not ‘invitations’. In Japanese there is a slight difference between the two, in the same way that there is in English. If you want to invite someone to do something, the most natural way would be to use
ませんか, a phrase that is similar to
ましょうか.
The difference here is that ‘won’t you do (A)?’ has a stronger nuance of being a direct invitation, while
ましょうか is closer to just ‘let’s do (A)!’