Let A be a 3 × 3 matrix with |A| = 4. If B is a matrix obtained from A by multiplying the second row by 3 and the third column by 1/2, then |B| is:
Correct: A
When a row of a matrix is multiplied by k, the determinant is multiplied by k. When a column is multiplied by k, the determinant is also multiplied by k. Starting with |A| = 4. Multiplying the second row by 3: |A'| = 3 × 4 = 12. Then multiplying the third column by 1/2: |B| = (1/2) × 12 = 6. Therefore |B| = 6.