Rigid body basics - Question about DETERMINANT

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?

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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