MathDB
matrix relation, every entry 1 matrix

Source: 2017 South Korea USCM P6

August 15, 2020
linear algebramatrixcollege contests

Problem Statement

Given a positive integer nn and a real valued n×nn\times n matrix AA. JJ is n×nn\times n matrix with every entry 11. Suppose AA satisfies the following relations. A+A^T = \frac{1}{n} J,   AJ = \frac{1}{2} J Show that Am−IA^m-I is an invertible matrix for all positive odd integer mm.
Back to ProblemsView on AoPS