Why does Newton’s law F = ma remain valid in different inertial frames?

Newton’s second law, $F=ma$, remains valid in different inertial frames due to the principle of Galilean invariance (or Galilean relativity).1

In classical mechanics, an inertial frame of reference is defined as a coordinate system that is neither accelerating nor rotating relative to the distant stars. The laws of motion are considered invariant—meaning they take the same form—across all such frames that are in uniform motion relative to one another.231

This consistency is maintained because the transformation between the coordinates of two inertial frames moving at a constant relative velocity is described by Galilean transformations. Under these transformations, the acceleration $a$ of a body remains the same for all inertial observers, and the forces acting upon the body are likewise consistent. Consequently, the relationship $F=ma$ holds true in every inertial frame, ensuring that the laws of mechanics are independent of the observer's uniform motion.341