Fast Inverse Matrix ?

I do my lighthing calculation in model space and hence hace to transform the light pos from world to model space fast.

The model transformation is basically M = [T] * [R]

Given a matrix:

Xaxisx YAxisx ZAxisx      Translationx
Xaxisy YAxisy ZAxisy       Translationy
Xaxisz YAxisz ZAxisz      Translationz
0            0         0                1

I wonder if a shortcut would be valid:

Xaxisx XAxisy XAxisz      -Translationx
Yaxisx YAxisy YAxisz      -Translationy
Zaxisx ZAxisy ZAxisz      -Translationz
0            0         0                1

Or do I have to do M = [R]-1 * [T]-1

yes, algebra allows that as far as R is orthogonal.

I believe that the inverted of a transformation matrix is:

R’ = transpose®
M = R’ * (- (R’ * T))

where R is the rotation part of the transformation matrix (the one with the Xaxisx etc) and T is the translation part (Translationx, Translationy, Translationz)

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