Leontief Inverse using stata - mata

#1
Dear all,
We can't manage to generate a Leontief Inverse matrix, below an example.


Given for example the following matrix converted from stata.

A=st_data(.,("a", "b","c", "d", "e","f"))

1 2 3 4 5 6
+-------------------------------+
1 | 8 4 5 2 3 1 |
2 | 9 5 5 5 9 9 |
3 | 9 3 3 3 5 6 |
4 | 3 10 8 8 6 10 |
5 | 6 1 4 5 9 10 |
6 | 4 7 3 3 5 3 |
+-------------------------------+


We try to generate a Leontief Inverse matrix by typing:

B = colsum(A)
C = luinv(diag(B))
D = A*C
L = luinv(I(6) - D)
L

we obtain

1 2 3 4 5 6
+-------------------------+
1 | . |
2 | . . |
3 | . . . |
4 | . . . . |
5 | . . . . . |
6 | . . . . . . |
+-------------------------+

Could someone suggest the right code to build a Leontief Inverse Matrix?

Thank you very much