 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-2/section-b/7/a/ii/solution

False. The cyclic property of the trace permits

A BC \mapsto BC A

, but not an arbitrary interchange. Even with

A

and

B

A = (1002), B = (1011), C = (0100) .

Then

Tr (A BC) = 1

and

Tr (B A C) = 2

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