Let I_A and I_B denote the moments of inertia of a body about two...

According to the parallel axis theorem, the moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis passing through its centre of mass and the product of its mass and the square of the perpendicular distance between the two axes.

Let axis $A$ pass through the centre of mass and axis $B$ be parallel to axis $A$ at a perpendicular distance $d$.

Then, $I_B = I_A + Md^2$

Since axis $B$ does not pass through the centre of mass, $d \neq 0$, which implies $Md^2 > 0$.

Therefore, $I_B > I_A$ or $I_A < I_B$.

Thus, if the axes are parallel, $I_A < I_B$ is always true.