Given a unit vector ||u|| = 1 in R3, let A = Au be the corresponding skew-symmetric

Question:

Given a unit vector ||u|| = 1 in R3, let A = Au be the corresponding skew-symmetric 3 x 3 matrix that satisfies A x = u x x, as in Exercise 9.4.39.
(a) Prove the Euler-Rodrigues formula etA = I + (sinr)A + (1 - cos t) A2. Use the matrix exponential series (9.46).
(b) Show that etA = I if and only if / is an integer multiple of 2π.
(c) Generalize parts (a) and (b) to a non-unit vector v ≠ 0.