In the Laplace or cofactor expansion of the determinant of an \(n\times n\) matrix, the number of operations:
\[\text{Addition: }\mathcal{A}(n)=n!-1\]
\[\text{Multiplication: }\displaystyle\mathcal{M}(n)=n!\sum_{k=1}^{n-1}\dfrac{1}{k!}=\lfloor(e-1)\cdot n!\rfloor-1\]
\[\text{Both combined: }\displaystyle\mathcal{T}(n)=n!\sum_{k=0}^{n-1}\dfrac{1}{k!}-1=\lfloor e\cdot n!\rfloor-2\]
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