Hello, I am trying to calculate the moment of inertia of a hyperboloid body, but wolfram always gives me the same input as output ! This is my input:

MomentOfInertia[
  ImplicitRegion[
    x^2/A^2 + y^2/A^2 - z^2/C^2 <= 1, {x, y, z}] /. {A -> 2, 
    C -> 6}] // MatrixForm

I want it as a symbolic calculation if it is posible. And can anybody explaines to me how can i apply the following moments formula on the hyperboloid body:

Underscript[\[Integral], {x,y,z}\[Element]reg](y^2+z^2  -x y -x z
-y x    x^2+z^2    -y z
-z x    -z y   x^2+y^2
)

Any help, please, it's very important to me.