n=3 m=3
random matrix A:
      -1.7     -0.259     -0.545 
    -0.298      -0.88      -0.96 
      -1.3      -1.33      -1.12 
G=
      2.16       1.13       1.24 
     -2.97       1.16      0.938 
    -0.648      -0.78      0.263 
b      =     0.862    0.00284       0.11 
x      =    -0.412      0.964     -0.758 
A*x   =     0.862    0.00284       0.11 
A*x-b=  2.22e-16   1.17e-16   2.08e-16 
AI=
    -0.435      0.658     -0.351 
       1.4       1.82      -2.23 
     -1.15      -2.92       2.16 
AI*A=
         1   1.11e-16  -5.55e-17 
         0          1  -4.44e-16 
         0   4.44e-16          1 

tall matrix:
n=4 m=3
random matrix A:
     -1.73      -1.09     -0.522 
    -0.385       -1.3      -1.35 
     -1.58      -1.04      -0.32 
     -1.54     -0.848      -1.49 
G=
      2.82       1.88       1.49 
     -2.92       1.06       1.04 
    -0.729      0.119       1.05 
    -0.576      0.201      -1.43 
b      =     0.801    0.00455      0.769      0.535 
x      =    -0.496    -0.0378      0.175 
A*x   =     0.805     0.0046      0.765      0.534 
A*x-b=   0.00356   5.93e-05   -0.00334  -0.000584 
AI=
    -0.214      0.557     -0.149     -0.397 
    -0.241     -0.823     -0.433      0.921 
       0.3     -0.108      0.454     -0.775 
AI*A=
         1   1.67e-16   2.22e-16 
         0          1  -2.22e-16 
         0          0          1