Matrix is a Warlock in my opinion. Since he literally has a demon inside of him in the normal universe it makes sense said demon would be his Patron.

His Backstory:

Matrix was born to a wealthy family but when he was 3 he grew ill. The only way to heal him was for his father to make a pact with a demon for Matrix. The demon turned into a magic gem and embedded himself into Matrix's chest. Matrix was then given his magical abilities. Matrix lost control of his powers one day and ate his parents on accident. He spent the rest of his life traveling across kingdoms and villages while making friends and growing a party.