A rigid body consists of three thin uniform rods, each of mass $m$ and length $2a$, held mutually perpendicular at their midpoints. Choose a coordinate system with axes along the rods.
show that the moment of inertia is the same for any axis passing through the origin.
Show I calculated $I_{xx} = I_{yy} = I_{zz} = 2/3ma^2$ and I showed $I_{zx} = I_{yz} = I_{xy} = 0$, So $I = 2/3ma^2(\cos^2(\alpha) + \cos^2(\beta) + \cos^2(\theta)$ where $\alpha,\beta,\theta$ are the angles between $x,y,z$-axis.
I understand for the people interested it's by construction the directional vectors will have unit length of 1,so those sum will add up to 1 so that is why it doesn't change !