This is strange; the code above works perfectly on my machines (Win7 / MMA9) and (Linux / MMA10):
In[1]:= m = {{1, 2, -3}, {0, -1, -6}}
m[[2]][[1]]
m[[2]][[1]] = 3
m
Out[1]= {{1, 2, -3}, {0, -1, -6}}
Out[2]= 0
Out[3]= 3
Out[4]= {{1, 2, -3}, {3, -1, -6}}
@Daniel Lichtblau: Thank you for pointing out the principal difference in the notation [[n,m]] and [[n]][[m]]! Once one knows it, it becomes quite obvious ...
