  The admittance matrix encodes the network topology and electrical parameters
of a power system in order to relate the current injection and voltage phasors.
Since admittance matrices are central to many power engineering analyses, their
characteristics are important subjects of theoretical studies. This paper
focuses on the key characteristic of \emph{invertibility}. Previous literature
has presented an invertibility condition for admittance matrices. This paper
first identifies and fixes a technical issue in the proof of this previously
presented invertibility condition. This paper then extends this previous work
by deriving new conditions that are applicable to a broader class of systems
with lossless branches and transformers with off-nominal tap ratios.
