Molecular Symmetry and Group Theory
Consider the effect of the C3 operation on the p orbitals of the B atom in BF3.
Although a pz orbital will remain unchanged, the px and py orbitals will end up rotated through an angle of 120°. The group character table (point group - D3h) confirms that the px and py orbitals are degenerate, but they are neither simply inverted or converted into each other by the C3 operation. In this case each orbital contributes cos 120° to the character of the matrix describing the operation.
Use the px, py and pz orbitals on the B atom as a basis to determine the characters of the matrices that describe the symmetry operations of BF3.