Stochastic matrix/Determinant/Behavior/Exercise

We want to establish statements about the determinant of a column stochastic $d\times d$-matrix.

1. Show that the determinant of a column stochastic matrix $M$ fulfills the relation

   $|detM|\le 1.$

2. Give an example of a column stochastic matrix that is not the identity matrix with

   $detM=1$

3. Let $d\ge 2$, and suppose that $M$ satisfies also the property that there exists a row where all entries are positive. Show

   $|detM|<1$

Create a solution