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  "body": "\n## Statement\n\nLet $A$ be a square matrix with entries in a field, for example the real numbers, and suppose that $A$ is [[invertible|0EB9N0S33C]].\nThen $\\det A \\neq 0$, and the [[determinant|00KDZRW4C0]] of the inverse is the reciprocal of the determinant of $A$:\n$$\\det(A^{-1}) = \\frac{1}{\\det A}.$$\n\n## Remarks\n\nThe determinant is multiplicative, and $A A^{-1} = I$ has determinant $1$.\nSo $\\det A \\cdot \\det(A^{-1}) = 1$, and the claim follows.\n",
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