For each of the following pairs of linear functions S, T: R2 → R2, describe the compositions S ○ T and T ○ S. Do the functions commute?
(a) S = counterclockwise rotation by 60°;
T = clockwise rotation by 120°
(b) S = reflection in the line y = x;
T = rotation by 180°
(c) S = reflection in the x axis; T = reflection in the y axis
(d) S = reflection in the line y = x; T = reflection in the line v = 2x
(e) S = orthogonal projection on the x-axis;
T = orthogonal projection on the y-axis
(f) S = orthogonal projection on the x-axis;
T = orthogonal projection on the line y = x
(g) S = orthogonal projection on the x-axis;
T = rotation by 180°
(h) S = orthogonal projection on the x-axis;
T = counterclockwise rotation by 90°
(i) S = orthogonal projection on the line y = -2x;
T = reflection in the line y = x