A Prove That The Twodimensional Rotation Matrix 129 Preserves Dot

(a) Prove that the two-dimensional rotation matrix (1.29) preserves dot products. (That is, show that Ay By + A z B z = Ay By + A z B z.)

(b) What constraints must the elements (Rij) of the three-dimensional rotation matrix (1.30) satisfy in order to preserve the length of A (for all vectors A)?

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