International Mathematics Competition
for University Students
2017

IMC2017: Day 1, Problem 1

1. Determine all complex numbers $\lambda$ for which there exist a positive integer $n$ and a real $n\times n$ matrix $A$ such that $A^2=A^T$ and $\lambda$ is an eigenvalue of $A$.

Proposed by: Alexandr Bolbot, Novosibirsk State University

Hint: Take square of $A^2=A^T$.

  Solution