Rotating 90 clockwise is the result of first reflecting across the main diagonal
and then reflecting across the vertical axis. Applying these two symmetries in the
other order results in a rotation of 270. Thus the rotations by 90 and 270 are
compositions of and symmetries in R C. Rotation by 180 is the composition
of the reflections across the horizontal and vertical axes (in either order). So this
rotation is in RC. Specifically, it is the result of reversing the orders of the rows
and the columns.