Chapter 4, Problem 4.20P

For trans-1,2-dichloroethylene, which has ${\text{C}}_{\text{2h}}$ symmetry,
a. List all the symmetry operations for this molecule.
b. Write a set of transformation matrices that describe the effect of each symmetry operationin the ${\text{C}}_{\text{2h}}$ group on a set of coordinates x, y, z for a point (your answer should consist offour $3\times 3$ transformation matrices).
c. Using the terms along the diagonal, obtain as many irreducible representations aspossible from the transformation matrices. You should be able to obtain three irreduciblerepresentations in this way, but two will be duplicates. You may check your results usingthe ${\text{C}}_{\text{2h}}$ character table.
d. Using the ${\text{C}}_{\text{2h}}$ character table, verify that the irreducible representations are mutuallyorthogonal,