Can PRINCE2 and SCRUM work together?

Probably, but I think it leads to idea-fall and Scrum factories.

Project idea's and requirements come from people with the least knowledge, but are committed to on a project road-map. The Scrum team here is just an iterative factory. Instead of giving teams high-level objectives and letting them learn and coming up with innovate solutions, what I think being Agile and Lean is all about.

Although unrelated to Prince2. See this video of Marty Cagan about idea-fall, only the build steps are iterative. Not the product design, which often leads to failed products.

I like his idea of doing Dual-track Scrum to facilating the discovery and delivery process.

In my opinion, Scrum and be used with PRINCE2 as described above. PRINCE2 just becomes the Management Layer above Scrum which is fine. PRINCE2 can be used to communicate with the management while Scrum is used by the teams who create and reviews the products.

An alternative to the PRINCE2 management layer is Scrum of Scrum.

A Prince2 practitioner might view Scrum as being contained neatly within the delivery level. A Scrum practitioner, on the other hand, might see Scrum extending into multiple aspects of the management and executive levels.

So, Prince2 can use parts of Scrum, but Scrum, as a complete package, may not be able to comfortably co-exist within Prince2. Scrum practitioners will tell you that it's either Scrum, or not Scrum, but not "partly-Scrum".

This is just wrong. It goes against the principles of Agile and SCRUM. PRINCE2 would be 'waste' in this context. There is no role and no need for it. It leads to a 'scrum-but' situation at its best.

Absolutely.

A project can remain Prince2 for as long as it adheres to the 7 prince2 principles. I have a detailed PDF on this found at Master Business Chronicles Blog

Absolutely!

Prince 2 is on project level, as Scrum can be done on 'managing product delivery' level within PRINCE2.

The Scrum process is all about delivery. Fast and effective delivery is key. Within PRINCE2 the delivery process is a black box. PRINCE2 is all about managing the project’s process.

This makes Scrum a natural fit to the PRINCE2 ‘Managing Product Delivery’ process. This also makes PRINCE2 the project management wrapper around Scrum. I think this is a great combination.

Here is more info on this: whitebook