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matrices problem

Source: Romanian District Olympiad 2015, Grade XI, Problem 3

September 26, 2018
Liniar algebraMatriceslinear algebra

Problem Statement

Find all natural numbers k≥1 k\ge 1 and n≥2, n\ge 2, which have the property that there exist two matrices A,B∈Mn(Z) A,B\in M_n\left(\mathbb{Z}\right) such that A3=On A^3=O_n and AkB+BA=In. A^kB +BA=I_n.
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