Why do different origins result in different principal moments of inertia?

[Geocentric]

Homework Statement

When I try finding the principal moments of inertia with respect to different origins for any arbitrary configuration(assuming that the inertia tensor is diagonalized), I end up getting different values. Intuitively, this is quite acceptable because the mass distribution is different with respect to axes corresponding to different origins. But in both the cases, the directions of principal axes are the same which is what really matter. I would like to have the thoughts of you guys as well on the statements I have made.

Homework Equations

The Attempt at a Solution

 

[diazona]

Sorry, but I don't understand exactly what your question is? And does this relate to a particular homework-type problem? (If not, perhaps someone should ask a mentor to move it to one of the physics discussion forums)

 

[Geocentric]

Let me be more specific. Consider 4 equal masses at the 4 corners of a square of side b. First I took one of the corners as the origin and found the principal moments of inertia to be Ixx=mb^2, Iyy=3mb^2, Izz=4mb^2 after solving the secular equation. Again, I found the principal moments of inertia but now with respect to the center of mass as origin as Ixx=mb^2, Iyy=mb^2, Izz=2mb^2. Now my question is, why do I get different values of principal moments of inertia?