However, none of this work utilizes the sum property for determinants [6]:
If A, B, and C are matrices with identical entries except that one row (column) of
C, say the kth, is the sum of the kth rows (columns) of A and B, then |A| + |B| =
|C|.
In this note we use this property to give a new proof of the following identity for the
Fibonacci numbers [1]: