We present a new method to compute the determinants of n × n (n ≥ 5)
matrices by reducing their sizes by four. To prove our results we use the so-called
“cornice determinants”, i.e, square determinants of order n (n ≥ 5) where, with
the exception of the first and last entries, the entries of the 2nd row and (n − 1)-
th row, as well the 2nd column and (n − 1)-th column are all zero. The method
introduced here has the advantage of reducing the size of a determinant by four,
and thus enabling their quicker and easier computation.