Difference between array and matrix and usage of "~"

Hello everyone:

I'm a maxima beginner and not very familiar with common lisp. I have 
some questions about the difference between array and matrix while I'm 
dealing with cross product calculation "~" in package "vect":

1. It seems like cross product "~" operator only works with array, not 
matrix, for when I input the following, error occurs:

(C1) load(vect)$
(C2) A : matrix([1,2,3], [4,5,6])$
(C3) row(A,1) ~ row(A,2);
(D3)                       [ 1  2  3 ] ~ [ 4  5  6 ]
(C4) express(row(A,1) ~ row(A,2));
~ USED WITH IMPROPER ARGUMENTS: [ 1  2  3 ] [ 4  5  6 ]
#0: EXPRESS1(expn=MATRIX([1,2,3]) ~ MATRIX([4,5,6]))(vect.mac line 165)
  -- an error.  Quitting.  To debug this try DEBUGMODE(TRUE);)

In vect.mac, the procedure related to "~" is:

    IF PIECE="~" THEN (
       ANS: INPART(EXPN,1),  EXPN:INPART(EXPN,2),
       IF LISTP(ANS) AND LISTP(EXPN) AND LENGTH(ANS)=LENGTH(EXPN) 
----------> line 165
          THEN (IF LENGTH(ANS)=2 THEN RETURN(ANS[1]*EXPN[2]
              -ANS[2]*EXPN[1]),
             IF LENGTH(ANS)=3 THEN RETURN([ANS[2]*EXPN[3]-
                ANS[3]*EXPN[2], ANS[3]*EXPN[1]-ANS[1]*EXPN[3],
                ANS[1]*EXPN[2]-ANS[2]*EXPN[1]])),
       ERROR("~ USED WITH IMPROPER ARGUMENTS:",ANS,EXPN))

We can see that "~" only accepts type list as its arguments. Then we 
will know array is implemented as list, but what about matrix, I may 
wonder.

2. zero vector returned from "~" simply "shrinks" to scalar zero:

(C1) [1,1,1] ~ [1,1,1];
(D1)                                               0

Why isn't it [0,0,0]?

Thank you very much for your help!