Question

Let A be an n × n matrix with the following properties:• In each column there is exactly one non-zero entry, and it’s equal to 1.• In each row there is exaclty one non-zero entry, and it’s equal to 1.Show that A is invertible. (Hint: Row reduction).

Answer 1

Solution

First, Notice that the determinant of A = 1

Therefore, A is non-singular

A is similar to the identity matrix, that is the rows and columns of A are independent

Therefore, A is Invertible