This document proposes a method for verifying web service compositions using Petri nets and transitive matrices. It presents a model for student online registration and examination web services. These services are represented as Petri nets which are then composed together. Deadlocks in the composition are detected using the transitive matrix of the Petri net. The algorithm computes the transitive matrix and uses it to derive reachable states and check for deadlocks. The method allows for verification of web service compositions and identification of potential deadlocks.