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Miklós Schweitzer 2012 P6

Source: Miklós Schweitzer 2012 P6

August 20, 2018
college contests

Problem Statement

Let A,B,CA,B,C be matrices with complex elements such that [A,B]=C,[B,C]=A[A,B]=C, [B,C]=A and [C,A]=B[C,A]=B, where [X,Y][X,Y] denotes the XY−YXXY-YX commutator of the matrices. Prove that e4πAe^{4 \pi A} is the identity matrix.
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