Let A, B be 2n×2n skew-symmetric matrices and let f be the characteristic polynomial of AB. Prove that the multiplicity of each root of f is at least 2.
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2010-15 Characteristic Polynomial,
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Let A, B be 2n×2n skew-symmetric matrices and let f be the characteristic polynomial of AB. Prove that the multiplicity of each root of f is at least 2.