Malus' Law on intensity?

Question

Does the intensity of the light source determine whether Malus' Law is obeyed or not?

Answer 1

Malus' Law calculates the transmitted intensity through  polarizers with an angle θ between the transmission directions of said polarizers. Thus being said, I would like to say the the light source intensity is an independent variable in this law.

In other words, as long as there is a light source (with whatever intensity), the corresponding transmitted intensity, given the required parameters, can always be determined.

This is my best interpretation of the Malus law.