Determinant of a matrix - Expanding by co-factors along other rows and columns
|A| | = | a21.c21 + a22.c22 + a23.c23 |
= | a21.(–1)2+1.M21 + a22.(–1)2+2.M22 + a23.(–1)2+3.M23 | |
= | – a21 M21 + a22 M22 – a23 M23 |
Similarly, expanding along 1st column, we have
Note that the + and – signs alternate in the expansions.