Sum of the minor and the cofactor of the element 6 in the determinant \(\begin{vmatrix}2 & 3 & 1\\ 4 & 5 & 6\\ 7 & 8 & 9\end{vmatrix}\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
The element 6 is in row 2, column 3. Its minor \(M_{23}\) is the determinant left after deleting row 2 and column 3:
\( \displaystyle M_{23} = \begin{vmatrix}2 & 3\\ 7 & 8\end{vmatrix} \)
\(M_{23} = 16 - 21 = -5\)
Its cofactor is
\(A_{23} = (-1)^{2+3}M_{23} = -(-5) = 5\)
\(M_{23} + A_{23} = -5 + 5 = 0\)