(Solution) - The product of two members of a group must be -(2025 Original AI-Free Solution)

Paper Details

The product of two members of a group must be a member of that group.
(a) List the members (the symmetry operations) of the group 2v, using the x, y, and z axes to specify the axis or plane with respect to which each symmetry operation is performed.
(b) For every possible product of two members of this group, state which symmetry operation it is equal to.
(c) The multiplication table of a group shows all possible products of two members of the group. Write down the multiplication table for 2v with each member of the group shown at the top and at the left of the table, and each entry in the table being the product of the member at the left of the row and the member at the top of the column of that entry.