Chapter 10, Problem 10B.6P

Interpretation Introduction

Interpretation:

The relationship $C_2^z{C}_2^y=C_2^x$, ${\sigma }^{xz}{C}_2^z=C_2^y$ and $i{C}_2^y={\sigma }^{xz}$ are to be validated by the use representatives of the operations of the group $D_{\text{2h}}$.

Concept introduction:

A symmetry operation is defined as an action on an object to reproduce an arrangement that is identical to its original spatial arrangement.  The group of symmetry operations of which at least one point is kept fixed is called point group.  The symmetry operations can be identity, rotation, reflection, inversion and improper rotation.