What should I study in order to be an inventor?

Brilliant question.

First and foremost, an Inventor is one who firstly and successfully creates or manufactures a form, method, device or anything before any one else does, that is useful either positively or negatively to mankind.

And to be an inventor, you will need to study courses basically relating to Science, Engineering, Technology and mathematics.

In Science, there's the like of medicine, and according to @Littleboy "there are lots of diseases that needs cure". And as a result, one needs to be strongly inclined in courses like chemistry, biology and also Mechanical engineering to be able to invent drugs which could help cure lots of diseases, and bear in mind that the knowledge of mechanical engineering will help in manufacturing the machines and equipment you would need to invent these drugs.

In Engineering, you might want to invent an automobile or any useful gadget or tech, in order to accomplish these, you need a strong knowledge of mathematics, physics and even chemistry, because in your quest to invent something related to this feed, you will need to do a lot of calculating and accurate calculation to be precise.

And for technology and mathematics, you need certain course that involves precise calculations and the likes.

As an inventor, you could also either invent something totally from scratch or may build upon an already established foundation. According to source "Alexander Graham Bell was being accredited with the invention of the "Telephone", but a number of other inventors suggested that Mr Alexander simply used their developed prototypes to create a working telephone."

So basically you just need to have an idea on what you would probably like to invent, then carefully choose a related field of study to boost and aid you to polish your idea before bringing it to reality.

CHEERS