MathDB
Every column of A has exactly one non-zero element

Source: IMO Longlist 1989, Problem 98

September 18, 2008
linear algebramatrixalgebra unsolvedalgebra

Problem Statement

Let A A be an n×n n \times n matrix whose elements are non-negative real numbers. Assume that A A is a non-singular matrix and all elements of A^{\minus{}1} are non-negative real numbers. Prove that every row and every column of A A has exactly one non-zero element.
Back to ProblemsView on AoPS