MathDB
Equality with two matrices implies nilpotence

Source: VJIMC 2024, Category I, Problem 2

April 14, 2024
matrixNilpotentlinear algebra

Problem Statement

Let nn be a positive integer and let AA, BB be two complex nonsingular n×nn \times n matrices such that A2B−2ABA+BA2=0.A^2B-2ABA+BA^2=0. Prove that the matrix AB−1A−1B−InAB^{-1}A^{-1}B-I_n is nilpotent.
Back to ProblemsView on AoPS