  A number $s$ is the sum of the entries of the inverse of an $n \times n, (n
\geq 3)$ upper triangular matrix with entries from the set $\{0, 1\}$ if and
only if $s$ is an integer lying between $2-F_{n-1}$ and $2+F_{n-1}$, where
$F_n$ is the $n$th Fibonacci number. A generalization of the sufficient
condition above to singular, group invertible matrices is presented.
