For trans-1,2-dichloroethylene, which has C2h symmetry,
a. List all the symmetry operations for this molecule.
b. Write a set of transformation matrices that describe the effect of each symmetry operation in the C2h group on a set of coordinates x, y, z for a point (your answer should consist of four 3 × 3 transformation matrices).
c. Using the terms along the diagonal, obtain as many irreducible representations as possible from the transformation matrices. You should be able to obtain three irreducible representations in this way, but two will be duplicates. You may check your results using the C2h character table.
d. Using the C2h character table, verify that the irreducible representations are mutually orthogonal.
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