Retrieving "Determinant Formula" from the archives

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1. Cofactor

   Linked via "determinant formula"

   This alternating sign pattern is often visualized as a checkerboard pattern applied to the matrix entries, where the top-left element $(1, 1)$ always carries a positive sign.
   The significance of the cofactor lies in the determinant formula. For an $n \times n$ matrix $\mathbf{A}$, the determinant can be calculated by summing the products of the elements of any single row or column with their corresponding cofactors:
   $$ \det(\mathbf{A}) = \sum{j=1}^{n} a{ij} C_{ij} \quad (\text{E…