Rotations and reflections have two remarkable properties: They preserve the length of ve...

Rotations and reflections have two remarkable properties: They preserve the length of vectors and the angle between vectors. (Draw figures illustrating these properties.) We will show that, conversely, any linear transformation T from that preserves length and angles is either a rotation or a reflection (about a line).

a. Show that if preserves length and angles, then the two column vectors v and w of A must be perpendicular unit vectors

c. Show that if a linear transformation T from preserves length and angles, then T is either a rotation or a reflection (about a line). See Exercise 17.