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Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).

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Let \(A, B\), and \(C\) be any \(n \times n\) matrices.
a) Show that \(\operatorname{trace}(A B)=\operatorname{trace}(B A)\).
b) Show that \(\operatorname{trace}(A B C)=\operatorname{trace}(C A B)=\operatorname{trace}(B C A)\).
c) \(\operatorname{trace}(A B C) \stackrel{?}{=} \operatorname{trace}(B A C)\). Proof or counterexample.
by ♦ Diamond (89,175 points) | 249 views

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