Matrix3.getNormalMatrix()

adjoint.glsl

// Use to transform normals with transformation of
// arbitrary non-uniform scales (including negative)
// and skewing. The code assumes the last column of m is 
// [0,0,0,1]. More info here:
// https://github.com/graphitemaster/normals_revisited

mat3 adjoint( in mat4 m )
{
    return mat3( 
     m[1][1]*m[2][2]-m[1][2]*m[2][1],
     m[1][2]*m[2][0]-m[1][0]*m[2][2],
     m[1][0]*m[2][1]-m[1][1]*m[2][0],
     m[0][2]*m[2][1]-m[0][1]*m[2][2],
     m[0][0]*m[2][2]-m[0][2]*m[2][0],
     m[0][1]*m[2][0]-m[0][0]*m[2][1],
     m[0][1]*m[1][2]-m[0][2]*m[1][1],
     m[0][2]*m[1][0]-m[0][0]*m[1][2],
     m[0][0]*m[1][1]-m[0][1]*m[1][0] );
}