XII Maths Chapter 4. Determinant | Page 8

Cofactors ( Minors with Signs )
Cofactor of an element aij , denoted by Aij is defined by Aij = (– 1 ) i + j Mij , where
Mij is minor of aij .
Determinant = a11 A11 + a12 A12 + a13 A13 If elements of a row ( or column ) are multiplied with cofactors of any other row ( or column ), then their sum is zero
a11 A21 + a12 A22 + a13 A23 = 0 a11 A31 + a12 A32 + a13 A33 = 0
Ad joint of a Matrix ( Cofactor - > Transpose )