[Insight-users] Degrees of freedom for affine transform?

[motes motes]

On page 407 in the itkSoftwareGuide its says that an affine transform has:

(N +1)*N

parameters. So in 3D the total number of parameters (DOF) would be:
(3+1)*3=12. Is it correct that these 12 parameters come from:

3 parameter from translation
3 parameter from scaling
3 parameter from rotation
3 parameter from shear

which gives a total of 12 parameters?