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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2008 • Question 5

Question

Math 6310 • Algebra Fall 2008 • Question 5

Let \(n\) be an integer. Let \(M\) be a square matrix with integer entries, such that the sum of the entries of each row equals \(n\). Prove that \(n\) divides the determinant of \(M\).

Raw LaTeX

Let \(n\) be an integer. Let \(M\) be a square matrix with integer entries, such that the sum of
the entries of each row equals \(n\). Prove that \(n\) divides the determinant of \(M\).

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization