Trace/Product of matrices/Exercise

Let ${}K$ be a field, and let ${}A$ denote an ${}m\times n$-matrix and let ${}B$ denote an ${}n\times m$-matrix over ${}K$. Show

${}\operatorname {trace} {\left(A\circ B\right)}=\operatorname {trace} {\left(B\circ A\right)}\,.$

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