It’s not uncommon for SCRUM Teams to have a SCRUM Master playing other role as well but for quite some reasons, Product Owner and SCRUM Master should not be the same person:
— Being a Product Owner is a full time job itself. Activities like creating User Stories, prioritizing Backlog, liaising with customer take a toll on Product Owner’s time and hence he/she will not be able to do justice to Scrum Master’s Role.
— Conflict of interests is another reason which prevents this. Product Owner will aim at getting maximum work done and might oversee the Scrum Process while Scrum Master has to ensure process is followed and the team is protected.
If one person tries to wear both the hats, it might end up in negligence of both the roles. There are teams where this has worked fine. But, ideally its best to keep these roles independent of each other.