Retrieving "Checkerboard Pattern" from the archives

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1. Cofactor

   Linked via "checkerboard pattern"

   $$ C{ij} = (-1)^{i+j} M{ij} $$
   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: