I've attached b.sobj which you can load to reproduce the error.
sage: ~b
---------------------------------------------------------------------------
<type 'exceptions.ZeroDivisionError'> Traceback (most recent call last)
/home/mike/<ipython console> in <module>()
/home/mike/matrix0.pyx in sage.matrix.matrix0.Matrix.__invert__()
<type 'exceptions.ZeroDivisionError'>: self is not invertible
sage: c = b.change_ring(RDF)
sage: ~c
[ 0.0277777777778 0.0277777777778 0.0277777777778 0.0277777777778 0.0277777777778 0.0277777777778]
[ 0.111111111111 -0.111111111111 0.0555555555556 -0.0555555555556 0.0555555555556 -0.0555555555556]
[ 0.0 0.0 0.0962250448649 0.0962250448649 -0.0962250448649 -0.0962250448649]
[ -0.0 -0.0 0.0962250448649 -0.0962250448649 -0.0962250448649 0.0962250448649]
[ 0.111111111111 0.111111111111 -0.0555555555556 -0.0555555555556 -0.0555555555556 -0.0555555555556]
[ 0.0277777777778 -0.0277777777778 -0.0277777777778 0.0277777777778 -0.0277777777778 0.0277777777778]