Abstract Petri nets serve as a model of computer systems which involve concurrent processes. Conflict and confluence are relations which can limit concurrency in many situations, while precedence between processes can completely negate any concurrency. This paper introduces several new matrices which show important relationships between transitions and places in Petri nets. These matrices are grouped into three types: conflict, confluence and precedence matrices. It is also shown that the matrices help to classify nets into widely known subclasses.