いきませんか vs いきますか


I have pretty much just started learning japanese and so far I can only recall
encountering いきますか as in "shall we go".

But while doing an exercise on marugoto I saw this sentence that confused me.

> A: あした にほんの えいがが ありますよ。
>
> B: いっしょに 見に いきませんか

So the question here is why is it いきませんか and not いきますか and why is it wrong to
answer

> B: いっしょに いきましょう

isn't that also grammatically correct as in lets go together?

