Yes, it is possible to create a 3x3 matrix using only the numbers -1, 0, and 1 such that all six row and column sums are distinct. Here is an example of such a matrix:

basic

1  1  0

-1  1  1

 0 -1 -1

Verification:

Row Sums: 1+1+0=2, -1+1+1=1, 0-1-1=-2

Column Sums: 1-1+0=0, 1+1-1=1, 0+1-1=0

In this matrix, all the row sums (2, 1, -2) and column sums (0, 1, 0) are distinct. Each row and each column sum to a unique value. This configuration meets the criteria you specified.