For each of the following linear transformations of
R2, determine the 2 × 2 matrix representing that transformation (simplify your matrix entries as much as possible):
(i) a reflection in the x-axis;
(ii) a rotation about the origin through a counterclockwise angle of Pie/2;
(iii) the transformation made by performing a reflection in the x-axis followed by
a rotation about the origin through a counterclockwise angle of Pie/2;
(iv) the transformation made by performing a rotation about the origin through
a counterclockwise angle of Pie/2 followed by a reflection in the x-axis.