On the vector space R3, let R denote counterclockwise rotation around the x axis by 90° and S counterclockwise rotation around the z axis by 90°.
(a) Find matrix representatives for R and S.
(b) Show that R ○ S ≠ S ○ R. Explain what happens to the standard basis vectors under the two compositions.
(c) Give an experimental demonstration of the noncommutativity of R and S by physically rotating a solid object, e.g., this book, in the prescribed manners.