Physical significance of singular matrix in two port network
It doesn't mean that the model breaks down, but it is usually a symptom that the model is idealized.

Consider the simplified common-emitter AC model for a BJT:







simulate this circuit &ndash; Schematic created using CircuitLab

It is clear that:

\begin{align*}
   I_2 &amp;= h_{fe} \cdot I_1 \\
   V_1 &amp;= h_{ie} \cdot I_1
\end{align*}

which can be rewritten in matrix form as:

\$
  \begin{bmatrix} V_1 \\ I_2 \end{bmatrix}
  =
  \begin{bmatrix} 
h_{11} &amp; h_{12} \\
h_{21} &amp; h_{22}
  \end{bmatrix}
  \cdot
  \begin{bmatrix} I_1 \\ V_2 \end{bmatrix}
  =
  \begin{bmatrix} 
h_{ie} &amp; 0 \\
h_{fe} &amp; 0
  \end{bmatrix}
  \cdot
  \begin{bmatrix} I_1 \\ V_2 \end{bmatrix}
\$

from which you can see the h-parameter matrix is singular, having the second column made up of zeroes, but still the model is valid, although really idealized, since it neglects the output conductance \$h_{oe}\$ and the \$h_{re}\$ coefficient.