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AB-BA=B^2A

Source: IMC 2019 Day 2 P9

July 31, 2019
linear algebraIMCcollege contests

Problem Statement

Determine all positive integers nn for which there exist n×nn\times n real invertible matrices AA and BB that satisfy ABBA=B2AAB-BA=B^2A.
Proposed by Karen Keryan, Yerevan State University & American University of Armenia, Yerevan