OnlineCBT
Mathematics · JEE | DETERMINANTS
हिन्दीGiven below are statements regarding minors and cofactors of an \( n \times n \) square matrix \( A = [a_{ij}] \) (\( n \ge 2 \)):\n(A) Minor of an element \( a_{ij} \) is a determinant of order \( n-1 \).\n(B) The cofactor \( A_{ij} \) is always equal to the minor \( M_{ij} \).\n(C) If elements of any row are multiplied with cofactors of any other row, then their sum is zero.\n(D) The value of the determinant is equal to the sum of the products of elements of any column with their corresponding cofactors.\nWhich of the above statements are correct?
View Answer & Solution
Correct answer · Option C
(A), (C) and (D) only
Explanation
Statement (B) is false because \( A_{ij} = (-1)^{i+j} M_{ij} \), which equals \( -M_{ij} \) when \( i+j \) is odd. Statements (A), (C), and (D) are all established properties of determinants.
