Chapter 4.2, Problem 12E

Let Y, P, and R be the yaw, pitch, and roll matrices given in equations (1), (2), and (3), respectively, and let $Q=YPR$ .
(a) Show that Y, P, and R all have determinants equal to 1.
(b) The matrix V represents a yaw with angle u. The inverse transformation should be a yaw with angle −u. Show that the matrix representation of the inverse transformation is $Y^T$ and that $Y^T=Y^{-1}$ .
(c) Show that Q is nonsingular and express $Q^{-1}$in terms of the transposes of Y, P, and R.