>> n=8;A = tril(ones(n))
A =
     1     0     0     0     0     0     0     0
     1     1     0     0     0     0     0     0
     1     1     1     0     0     0     0     0
     1     1     1     1     0     0     0     0
     1     1     1     1     1     0     0     0
     1     1     1     1     1     1     0     0
     1     1     1     1     1     1     1     0
     1     1     1     1     1     1     1     1
>> Ainv=inv(A)
Ainv =
     1     0     0     0     0     0     0     0
    -1     1     0     0     0     0     0     0
     0    -1     1     0     0     0     0     0
     0     0    -1     1     0     0     0     0
     0     0     0    -1     1     0     0     0
     0     0     0     0    -1     1     0     0
     0     0     0     0     0    -1     1     0
     0     0     0     0     0     0    -1     1
>> n=12;A = tril(ones(n)); Ainv=inv(A)
Ainv =
     1     0     0     0     0     0     0     0     0     0     0     0
    -1     1     0     0     0     0     0     0     0     0     0     0
     0    -1     1     0     0     0     0     0     0     0     0     0
     0     0    -1     1     0     0     0     0     0     0     0     0
     0     0     0    -1     1     0     0     0     0     0     0     0
     0     0     0     0    -1     1     0     0     0     0     0     0
     0     0     0     0     0    -1     1     0     0     0     0     0
     0     0     0     0     0     0    -1     1     0     0     0     0
     0     0     0     0     0     0     0    -1     1     0     0     0
     0     0     0     0     0     0     0     0    -1     1     0     0
     0     0     0     0     0     0     0     0     0    -1     1     0
     0     0     0     0     0     0     0     0     0     0    -1     1

>> n=10;A = triu(ones(n))             
A =
     1     1     1     1     1     1     1     1     1     1
     0     1     1     1     1     1     1     1     1     1
     0     0     1     1     1     1     1     1     1     1
     0     0     0     1     1     1     1     1     1     1
     0     0     0     0     1     1     1     1     1     1
     0     0     0     0     0     1     1     1     1     1
     0     0     0     0     0     0     1     1     1     1
     0     0     0     0     0     0     0     1     1     1
     0     0     0     0     0     0     0     0     1     1
     0     0     0     0     0     0     0     0     0     1
>> inv(A)
ans =
     1    -1     0     0     0     0     0     0     0     0
     0     1    -1     0     0     0     0     0     0     0
     0     0     1    -1     0     0     0     0     0     0
     0     0     0     1    -1     0     0     0     0     0
     0     0     0     0     1    -1     0     0     0     0
     0     0     0     0     0     1    -1     0     0     0
     0     0     0     0     0     0     1    -1     0     0
     0     0     0     0     0     0     0     1    -1     0
     0     0     0     0     0     0     0     0     1    -1
     0     0     0     0     0     0     0     0     0     1