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  "body": "\n## Statement\n\nLet $R$ be a commutative ring and let $A$ be an $n \\times n$ matrix over $R$.\nThen $\\tr(A^T) = \\tr A$, where $A^T$ is the [[transpose|09DXWYRD43]] of $A$ and $\\tr$ is the [[trace|0XC1RDBY7A]].\n\n## Remarks\n\nThe transpose does not move the entries on the main diagonal, so the sum of the diagonal entries stays the same.\nFor a complex matrix, $\\tr(A^*) = \\overline{\\tr A}$.\n\n## Explanations\n\n### L1 human\n\nTransposing flips a matrix over its diagonal.\nThe diagonal itself does not move.\nSo the trace, which only sees the diagonal, does not change.\n",
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