MathDB

98

Part of 1989 IMO Longlists

Problems(1)

Every column of A has exactly one non-zero element

Source: IMO Longlist 1989, Problem 98

9/18/2008
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.
linear algebramatrixalgebra unsolvedalgebra