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  "body": "\n## Statement\n\nLet $K$ be a commutative ring, let $A$ be an $n \\times n$ matrix over $K$, and let $c \\in K$.\nLet $B$ be the matrix that results when one row of $A$ is multiplied by $c$.\nThen $\\det B = c \\det A$, where $\\det$ is the [[determinant|00KDZRW4C0]].\n\n## Remarks\n\nThis is a special case of [[linearity in each row|0PPG793642]].\nIt describes the effect of the scaling [[row operation|04XWH28452]] on the determinant.\nScaling all $n$ rows gives $\\det(cA) = c^n \\det A$, see [[the determinant of a scalar multiple|01EXSMK864]].\n\n## Explanations\n\n### L1 human\n\nIf we stretch one edge of a box by the factor $c$, then its volume is multiplied by $c$.\nThe determinant behaves in the same way.\nFor example, doubling one row doubles the determinant.\n",
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