MathDB
Freshman's dream for matrices

Source: SEEMOUS 2024, Problem 2

April 16, 2024
college contestslinear algebra

Problem Statement

Let A,B∈Mn(R)A,B\in\mathcal{M}_n(\mathbb{R}) two real, symmetric matrices with nonnegative eigenvalues. Prove that A3+B3=(A+B)3A^3+B^3=(A+B)^3 if and only if AB=OnAB=O_n.
Back to ProblemsView on AoPS