(a) Prove that the two-dimensional rotation matrix (Eq. 1.29) preserves dot products. (T...

(a) Prove that the two-dimensional rotation matrix (Eq. 1.29) preserves dot products. (That is, show that

(b) What constraints must the elements (R_{i j} ) of the three-dimensional rotation matrix (Eq. 1.30) satisfy, in order to preserve the length of A (for all vectors A)?

Reference equation 1.30

Reference equation 1.29