Let Y, P, and R be the yaw, pitch, and roll matrices given in equations (1), (2)

Question:

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