If we expand the determinant of a matrix 
using determinant
expansion by minors, first in terms of the minors of
order 
formed from any 
rows, with their complementaries, and second in terms of the minors
of order 
formed from any 
columns (
),
with their complementaries; then the sum of the 
terms of the second expansion which have in common
the elements in the intersection of the selected 
rows and 
columns is equal to the sum of the 
terms of the first expansion which have for one factor the
minors of the 
th
order formed from the elements in the intersection of the selected 
rows and 
columns.
Schweins's Theorem
See also
Determinant, Determinant Expansion by Minors, MinorExplore with Wolfram|Alpha
References
Muir, T. "Schweins's Theorem." §141 in A Treatise on the Theory of Determinants. New York: Dover, pp. 124-125, 1960.Referenced on Wolfram|Alpha
Schweins's TheoremCite this as:
Weisstein, Eric W. "Schweins's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SchweinssTheorem.html