The BF₃ molecule is planar with bond angles of 120^◦.
(a) List the symmetry operators that belong to this molecule. We place the molecule in the x–y plane with the boron atom at the origin and one of the fluorine atoms on the x axis. Call the fluorine atoms a, b, and c starting at the x axis and proceeding counterclockwise around the x–y plane. The symmetry elements are: a threefold rotation axis, three vertical mirror planes containing a fluorine atom, the horizontal mirror plane, and three twofold rotation axes containing a fluorine atom.
(b) Find the three-dimensional matrices corresponding to the operators:

(i) Ĉ_3(z).
(ii) σ̂_a.
(iii) Ĉ_2a.
(c) Find the following operator products:
(i) Ĉ_3(z) σ̂_a.
(ii) σ̂_a σ̂_h.
(iii) Ĉ_3(z) Ĉ_2a.