This is a small discrepancy, but calling inv() for the exceptional value of NaN produces different results in Matlab and Octave.  In my opinion, Matlab is more consistent in always returning a NaN result.  Octave will return Inf occasionally, which seems incorrect because the input has been changed from Not-a-Number to a numerical value (Inf).

In Octave:

octave:13> x = nan (2,2)
x =

   NaN   NaN
   NaN   NaN

octave:14> y = inv (x)
warning: matrix singular to machine precision, rcond = nan
y =

   NaN   NaN
   NaN   NaN

octave:15> y = inv (single (x))
warning: matrix singular to machine precision, rcond = nan
y =

   NaN     0
   NaN   NaN

octave:16> y = inv (complex (single (x), ones (2,2)))
warning: matrix singular to machine precision
y =

   Inf   Inf
   Inf   Inf

octave:17> y = inv (complex (x, ones (2,2)))
warning: matrix singular to machine precision
y =

   Inf   Inf
   Inf   Inf

In Matlab R2022a:

>> x = nan (2,2)

x =

   NaN   NaN
   NaN   NaN

>> y = inv (x)
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.


y =

   NaN   NaN
   NaN   NaN

>> inv (single (x))
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.


ans =

  2×2 single matrix

   NaN   NaN
   NaN   NaN

>> inv (complex (single (x), ones (2,2)))
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.


ans =

  2×2 single matrix

      NaN +    NaNi      NaN +    NaNi
      NaN +    NaNi      NaN +    NaNi

>> inv (complex (x, ones (2,2)))
Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.


ans =

      NaN +    NaNi      NaN +    NaNi
      NaN +    NaNi      NaN +    NaNi