>> A=[1 2 3;4 5 6;7 8 9]

A =

     1     2     3
     4     5     6
     7     8     9

>> det(A)

ans =

     0

>> cross([1,2,3],[4,5,6])

ans =

    -3     6    -3

>> B=A

B =

     1     2     3
     4     5     6
     7     8     9

>> B(3,:)=[5,2,1]

B =

     1     2     3
     4     5     6
     5     2     1

>> inv(B)

ans =

    1.1667   -0.6667    0.5000
   -4.3333    2.3333   -1.0000
    2.8333   -1.3333    0.5000

>> inv(B)*[0;0;0]

ans =

     0
     0
     0

>> inv(B)*[0;0;1]

ans =

    0.5000
   -1.0000
    0.5000

>> inv(B)*[0;0;2]

ans =

    1.0000
   -2.0000
    1.0000

>> b=[0;3;6]

b =

     0
     3
     6

>> x=inv(A)*b
Warning: Matrix is close to singular or badly scaled.
         Results may be inaccurate. RCOND = 1.541976e-18.

x =

     4
    -8
     4

>> A*x

ans =

     0
     0
     0

>> inv(B)*b

ans =

    1.0000
    1.0000
   -1.0000

>> A*[1;1;-1]

ans =

     0
     3
     6

>>