Chapter 2 - Matrices - 2.1 Operations with Matrices - 2.1 Exercises - Page 50: 68

\begin{align*} \operatorname{Tr}(AB)&=\sum_{i=1}^n\left(\sum_{k=1}^na_{ik}b_{ki}\right)\\ &=\sum_{i=1}^n\left(\sum_{k=1}^nb_{ik}a_{ki}\right)\\ &=\operatorname{Tr}(BA). \end{align*}

\begin{align*} \operatorname{Tr}(AB)&=\sum_{i=1}^n\left(\sum_{k=1}^na_{ik}b_{ki}\right)\\ &=\sum_{i=1}^n\left(\sum_{k=1}^nb_{ik}a_{ki}\right)\\ &=\operatorname{Tr}(BA). \end{align*}