How to determine if a matrix is a 3D cartesian rotation matrix

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If you have a 3x3 matrix and you want to determine whether it can be a 3D cartesian rotation matrix or not, what's the best and quickest way to determine this? What's the best starting point?

I'm not sure where to start.

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The sufficient checks are:

  1. Check that matrix is orthogonal $MM^T=I$
  2. Check that matix isn't a reflection: $\det M>0$