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6

Part of 2016 Korea USCM

Problems(1)

Prove that two 2*2 matrices have common eigenvector

Source: 2016 South Korea USCM P6

8/16/2020
AA and BB are 2×22\times 2 real valued matrices satisfying \det A = \det B = 1,  \text{tr}(A)>2,  \text{tr}(B)>2,  \text{tr}(ABA^{-1}B^{-1}) = 2 Prove that AA and BB have a common eigenvector.
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