Mathematics · JEE | DETERMINANTS

Consider the following statements regarding a square matrix \( A = [a_{ij}]_{3 \times 3} \) with minor \( M_{ij} \) and cofactor \( A_{ij} \):\n(A) Minor \( M_{ij} \) of an element is obtained by deleting its \( i \)-th row and \( j \)-th column.\n(B) The cofactor is defined as \( A_{ij} = (-1)^{i+j} M_{ij} \).\n(C) If elements of a row are multiplied with cofactors of any other row, their sum is equal to \( |A| \).\n(D) \( \sum_{j=1}^3 a_{1j} A_{1j} = \sum_{i=1}^3 a_{i2} A_{i2} = |A| \). \nChoose the correct answer from the options given below:

1. A
   (A), (B) and (D) only
2. B
   (B), (C) and (D) only
3. C
   (A), (B) and (C) only
4. D
   All (A), (B), (C) and (D)