Teaching Tip: When a Matrix and Its Inverse Are Stochastic
Jiu Ding, Noah H. Rhee · College Mathematics Journal · 2013
SummaryA stochastic matrix is a square matrix with nonnegative entries and row sums 1. The simplest example is a permutation matrix, whose rows permute the rows of an identity matrix. A permutation matrix and its inverse are both stochastic. We prove the converse, that is, if a matrix and its inverse are both stochastic, then it is a permutation matrix.