(a) Show that the transformation of coordinates in eqn (18.40) and the inverse relation in eqn...

(a) Show that the transformation of
coordinates in eqn (18.40) and the inverse relation in eqn (18.45) may be
written in matrix form as

where A is the matrix defined in eqn
(E.27). (b) Verify that matrix A is both canonical and orthogonal, i.e., that
it satisfies both s = AT s A and AT = A −1.