What could be wrong with my approach to finding principal moments of inertia?

Geocentric
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Homework Statement


I have a question on finding the principal moments of inertia of a discrete set of mass points on a plane. If I choose one of the mass points as the origin, I always end up having a diagonal matrix for the inertia tensor for any configuration. Isn't that weird? I sense something wrong with my solution. Could someone please help me?

Homework Equations


The Attempt at a Solution

 
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Never mind. I get it now guys.
 

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