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Fastest inversion of 3x3 matrix with rotation AND scale

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What''s the best (fastest) algorithm to invert a 3x3 matrix that contains information about the rotation AND scale. I need this to retrieve the world coordinates from local coordinates in OpenGL, this matrix comes from the modelview. If you only have rotation, you can use the transpose of the 3x3 matrix but with scale, it doesn''t work anymore. Should I use Cramer''s rule and compute the determinants with cofactors or is there a better way to handle the scale ?

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