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  "body": "\n## Statement\n\nLet $K$ be a commutative ring and let $a, b, c, d \\in K$.\nThen\n$$\\det \\begin{pmatrix} a \u0026 b \\\\ c \u0026 d \\end{pmatrix} = ad - bc,$$\nwhere $\\det$ is the [[determinant|00KDZRW4C0]].\n\n## Remarks\n\nThis is the [[Leibniz formula|016PE4VZ8Q]] for $n = 2$, with the identity and one transposition.\nOver $\\R$, $\\abs{ad - bc}$ is the area of the parallelogram spanned by the columns $(a, c)$ and $(b, d)$.\nFor example, $\\det \\begin{pmatrix} 1 \u0026 2 \\\\ 3 \u0026 4 \\end{pmatrix} = 4 - 6 = -2$.\n\n## Explanations\n\n### L1 human\n\nThe determinant of a $2 \\times 2$ matrix is the product of the main diagonal minus the product of the other diagonal.\nIt is zero exactly when one column is a multiple of the other, over a field.\nThen the matrix squeezes the plane onto a line or a point.\n",
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