The trace of an n × n matrix A = | a;| is the sum of the entries on its main diagonal and is denot 1). That is, tr(A)= a11 + a22 +… + ann. Prove that if A and B are n x n matrices, then tr(AB)=t

Elementary Linear Algebra (MindTap Course List)
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Chapter2: Matrices
Section2.1: Operations With Matrices
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4. The trace of an n × n matrix A = | a¡j| is the sum of the entries on its main diagonal and is denoted by
tr(A). That is, tr(A)= a11 + a22 + …*
+ ann. Prove that if A and B are n × n matrices, then tr(AB)=tr(BA).
Transcribed Image Text:4. The trace of an n × n matrix A = | a¡j| is the sum of the entries on its main diagonal and is denoted by tr(A). That is, tr(A)= a11 + a22 + …* + ann. Prove that if A and B are n × n matrices, then tr(AB)=tr(BA).
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