Difference between real fft and complex fft with imaginary part of zero in fftw?
I haven't tried this myself but I think it's just a problem of ordering the output data. In the real-to-complex case, your output matrix is not a $3\times 3$ matrix, but - due to the implied symmetry - a $3 \times 2$ matrix. So re-arranging your output gives

 36            -4.5+2.59808i
-13.5+7.79423i  0
-13.5-7.79423i  0  


where the "missing" third column would just be the complex conjugate of the second column. This is also explained here.