# Inverse of infinite matrices with more than one infinite row

If an infinite matrix $A$ is row column-finite and has inverse, but the inverse $A^{-1}$ (that is $AA^{-1}=I$ )is not row-finite (only column-finite). My question is:

Is there is a possibility that $A^{-1}$ only has one row which is not finite. or always need to have more than one infinite row?