International Mathematics Competition
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2023

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IMC2023: Day 1, Problem 2

Problem 2. Let \(\displaystyle A\), \(\displaystyle B\) and \(\displaystyle C\) be \(\displaystyle n\times n\) matrices with complex entries satisfying

\(\displaystyle A^2 = B^2 = C^2 \quad \text{and} \quad B^3 = ABC + 2I. \)

Prove that \(\displaystyle A^6 = I\).

Mike Daas, Universiteit Leiden

Hint: Factorize \(\displaystyle B^3-ABC\).

    

IMC
2023

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