Table of Contents - 11.3.4. Laplace expansion of determinants (special case)

According to Wikipedia ("Laplace expansion", 08-Mar-2019,
https://en.wikipedia.org/wiki/Laplace_expansion) "In linear algebra, the
Laplace expansion, named after Pierre-Simon Laplace, also called cofactor
expansion, is an expression for the determinant det(B) of an n x n -matrix B
that is a weighted sum of the determinants of n sub-matrices of B, each of
size (n-1) x (n-1)". The expansion is usually performed for a row of matrix B
(alternately for a column of matrix B). The mentioned "sub-matrices" are the
matrices resultung from deleting the i-th row and the j-th column of matrix
B. The mentioned "weights" (factors/coefficients) are the elements at
position i and j in matrix B. If the expansion is performed for a row, the
coefficients are the elements of the selected row.

In the following, only the case where the row for the expansion contains only
the zero element of the underlying ring except at the diagonal position. By
this, the sum for the Laplace expansion is reduced to one summand, consisting
of the element at the diagonal position multiplied with the determinant of
the corresponding submatrix, see smadiadetg or smadiadetr.