For correctness one should mention the iteration step in operations: after having subtracted R2(0) from R2(0) the new R2 is R2(1) = {0,0,0}. Subtracting then R3(0) the new R2 is R2(2) = R2(1) - R3(0) = -R3(0). This counting considers row operations only and does not fit to the general case. But let's say you mean

 [{
{1,8,3},
{4,4,6}, - R2(0) - R3(0)
{4,8,5}  - R3(0) - R2(0)
}]

i.e. all operations have to take place with the initial rows, then it means to exchange R2 with R3 and have both negative

In[80]:= Clear[mKnill]
mKnill={{1,8,3},{4,4,6},{4,8,5}};
In[83]:= {{1,0,0},{0,0,-1},{0,-1,0}}.mKnill // MatrixForm
Out[83]//MatrixForm= (1 8   3
-4  -8   -5
-4  -4   -6
)