1. Which of the five linear transformations in Exercise II.1 on page 19 are rigid? Which ones are both rigid and orientation-preserving?
2. Let M = (u, v), that is, M =ho w that the linear transformation represented by the matrix M is rigid if and only ifand u · v = 0.Pr ove that if M represents a rigid transformation, then det (M) = ±1. A matrix M of the type in the previous exercise is called an orthonormal matrix.