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  "body": "\n## Statement\n\nLet $K$ be a commutative ring and let $a, b, c, d, e, f, g, h, i \\in K$.\nThen\n$$\\det \\begin{pmatrix} a \u0026 b \u0026 c \\\\ d \u0026 e \u0026 f \\\\ g \u0026 h \u0026 i \\end{pmatrix} = aei + bfg + cdh - ceg - bdi - afh,$$\nwhere $\\det$ is the [[determinant|00KDZRW4C0]].\n\n## Remarks\n\nCopy the first two columns to the right of the matrix.\nThen the three positive terms are the products along the diagonals that go down to the right.\nThe three negative terms are products along the diagonals that go up to the right in the same picture.\nThis rule is the [[Leibniz formula|016PE4VZ8Q]] for $n = 3$; it has no analogue with diagonals for $n \\ge 4$.\n\n## Explanations\n\n### L1 human\n\nThe rule of Sarrus is a memory aid for $3 \\times 3$ determinants.\nWrite the first two columns again to the right of the matrix.\nAdd the three products down to the right, and subtract the three products up to the right.\n",
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