I was told that the mass action law $$np = n_i^2$$ only applies to compensated semiconductors and intrinsic semiconductors, and it does not apply to n-type or p-type semiconductors. Is this true? I also heard the argument that the hole concentration decreases as the electron concentration increases in case of a n-type doping, therefore the mass action law is still applicable. I am not sure which is right, but I am sure I am missing something here.
When solving problems such as the one below
The electron concentration in silicon at $T=300\text{ K}$ is $n_0 = 2\times 10^5 \text{ cm} ^{-3}$.
(a) Determine the position of Fermi level with respect to the valence band energy level.
(b) Determine $p_0$.
(c) Is this n- or p-type material?
Source: Semiconductor physics and devices, Donald A. Neamen
I am not sure whether I can apply the mass action law or not. For example, could part (b) solved using the mass action law since the electron concentration is given? $$p_o = n_i^2/n_o$$
Please help me understand when I can or cannot apply the mass action law.