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Romania District MO 2022 Grade 11 P2

Source: Romania District MO 2022 Grade 11

March 27, 2022
matrixcollege contestsromania

Problem Statement

Let A,B∈M3(R)A,B\in\mathcal{M}_3(\mathbb{R}) de matrices such that A2+B2=O3.A^2+B^2=O_3. Prove that det⁡(aA+bB)=0\det(aA+bB)=0 for any real numbers aa and b.b.
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