Learn Swedish: Det spelar ingen roll.

This is a set idiom. Instead of using a single verb like the English word matter, Swedish literally says it plays no role, using the words spelar (plays) and roll (role). It is similar to the English expression it plays no part.

Why do we use ingen here instead of inte?

The word ingen means no or not any when placed directly before a noun. Here, you are literally saying it plays no role. You could technically use inte by saying Det spelar inte någon roll (It does not play any role), but using ingen is much more direct and common.

Why is it ingen and not inget?

The noun roll is an en-word (en roll), so its matching adjective must be the en-word form ingen. If the noun in the sentence were an ett-word, you would use inget instead.

Can I use Det spelar ingen roll to mean I don't mind?

Yes, this is the perfect phrase for that! If a friend asks whether you prefer coffee or tea, replying Det spelar ingen roll is the standard way to say that you do not mind or that either choice is fine.