# A Tricky Linear Algebra Example

by David Sprows

College Mathematics Journal
January, 2008

Subject classification(s): Algebra and Number Theory | Linear Algebra | Vector Spaces
Applicable Course(s): 3.8 Linear/Matrix Algebra

In this article a classroom "trick" involving square arrangements of natural numbers is used to motivate a discussion of a special class of matrices. In particular, a basis is obtained for those $$n$$ by $$n$$ square matrices with the property that if $$n$$ entries are selected from the matrix so that no two values are in the same row or the same column, then the sum of these $$n$$ entries will always be the same.

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