Problem 3 In each crystallographic group, the group operation . means the combination of two symmetry operations. For example, A . B means to apply the symmetry operation defined by B first and then to apply the symmetry operation defined by A. Explain whether and why (or why not) all the translation operations defined by a 2D square lattice (t1 = ax, t2 = ay. x and y are unit vectors in a Cartesian coordinate system) plus the group operation defined above can form a crystallographic group. tz = ay XD =