  Context: Magnetic fields can play crucial roles in high-mass star formation.
Nonetheless, the significance of magnetic fields at various scales and their
relationship with gas structures is largely overlooked. Aims: Our goal is to
examine the relationship between the magnetic field and molecular gas
structures within the Orion A giant molecular cloud at different scales and
density regimes. Methods: We assess the gas intensity structures and column
densities in Orion A by utilizing $^{12}$CO, $^{13}$CO, and C$^{18}$O from
Nobeyama observations. Through comparing Nobeyama observations with
{\it{Planck}} polarization observations on large scales ($\sim0.6$ pc) and JCMT
polarization observations on small scales ($\sim0.04$ pc), we investigate how
the role of magnetic fields change with scale and density. Results: We find a
similar trend from parallel to perpendicular alignment with increasing column
densities in Orion A at both large and small spatial scales. Besides, when
changing from low-density to high-density tracers, the relative orientation
preference changes from random to perpendicular. The self-similar results at
different scales indicate that magnetic fields are dynamically important in
both cloud formation and filament formation. However, magnetic fields
properties at small scales are relative complicated, and the interplay between
magnetic field and star-forming activities needs to be discussed case-by-case.
