Chapter 2 - Matrices and Systems of Linear Equations - 2.2 Matrix Algebra - Problems - Page 136: 25

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Let $A=[a_{ij}]$ and $B=[a_{ij}]$. A and B are both $n \times n$ matrices, then $tr(AB)=\sum\limits_{k=1} (\sum\limits_{i=1} a_{ki}b_{ik})=\sum\limits_{k=1}(\sum\limits_{i=1} b_{ik} a_{ki})=\sum\limits_{i=1}(\sum\limits_{k=1} b_{ik} a_{ki})=tr(AB)$