Jack Milunsky wrote about the Top Ten Activities of a Product Owner. His post included number 6:
6. Participates in the daily Scrums, Sprint Planning Meetings and Sprint Reviews and Retrospectives. There’s always a lot going on and always an excuse to miss the meetings. But each of these Scrum ceremonies is another chance for the Product Owner to inspect and adapt. And as a result being present at these ceremonies is tantamount to success.
In reply, a number of folks commented that they didn't like the idea of a Product Owner attending Sprint Retrospectives. They don't consider the PO as part of their team. When Esther and I teach our workshop "Leading Agile Retrospectives" and, pretty much whenever I'm someplace where people want to get their retrospective questions answered, this question always surfaces. Who attends?
Yes, the team uses the Retrospective as time to inspect and adapt their practices, methods, teamwork, and other work processes. Retrospectives answer the team questions, "How's it going, really? Why? What will we do about that?" So, Agile Retrospectives serve the team.
The answer to "Who attends?" depends on who is participating on a daily, or near-daily, basis as part of the team. If my team's Product Owner was engaged with my team fulfilling all the ten activities Jack describes, I'd want that Product Owner in our Retrospective as often as possible. They could contribute insights and perspectives about the work that could prove very useful to my team.
On the other hand, if the Product Owner is more of an absentee landlord, coming around just for Release Planning and Sprint Reviews, and hard to find when we need clarification, then I'd think twice. It would depend largely on the focus of a given Retrospective and what the PO's views could contribute.
As usual, no hard and fast rules exist. And, I'd appreciate, value, and include a Product Owner who is as involved as Jack describes.