How can I determine whether a conference is reputable?
I'm assuming you are really asking how to check whether a conference is reputable (meaning not a scam), not how to check whether a conference is actually good.

Short answer: If you don't recognize the conference or its organizers, stay away.

You should already know a relatively short list of established, reputable conferences in your research area.  If you don't, ask your advisor to give you such a list.  (If your advisor doesn't know, you need a new advisor.)

If this conference isn't on that list, it might still be reputable, but either very new or slightly outside your research area.  In that case, take a serious look at the organizing committee.  If the members of the organizing committee are well-known active researchers, the conference is probably fine.  Otherwise, it's probably a scam.

You mention that you were invited to submit to the conference.  At least in computer science, such invitations are almost unheard of; conferences are normally advertised by impersonal calls for papers.  Did the invitation come from someone you already know, at least professionally?  Does the invitation mention specific technical details of your work (more than just a paper title)?  If you answered "No" to both these questions, the conference is almost certainly a scam.