Rigid body basics - Question about DETERMINANT

Course Support Basic Arm Kinematics
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Given that DETERMINANT represents the degree of DEFORMATION of SPACE, is this statement “One last property of the Rigid Body Rotation Matrix is that the DETERMINANT has to be 0 ALWAYS.” right?

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If determinant is zero means

  1. Matrix is a singular matrix
  2. It cannot be invertible, but rotation matrix can be inverted

Rotations preserve volume so determinant has to be 1.

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