Theorem (already this post looks different than usual ‘cause it has a theorem):
If an invertible matrix A had constant row sums of k, then the inverse of A has constant row sums of 1/k.
Proof (Oh, no. A proof. Just when this blog looked like it was just fun stuff):
Let A be an m-by-m invertible matrix with constant row sums of k. Let B be the inverse of A. Now, AB = I and the diagonal elements of I are all 1. Note that I has a constant row sum of 1. Hmmm. Let