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Mathematics · JEE | DETERMINANTS
हिन्दीMatch List-I with List-II for a non-singular matrix \( A \) of order \( 3 \) with \( |A| = 2 \): \n List-I (Matrix Expression) List-II (Determinant Value) A \( |A^2| \) I \( 4 \) B \( |\text{adj } A| \) II \( 16 \) C \( |\text{adj }(\text{adj } A)| \) III \( 8 \) D \( |2A| \) IV \( 16 \) \n Choose the correct answer from the options given below:
Match List-I with List-II for a non-singular matrix \( A \) of order \( 3 \) with \( |A| = 2 \):
\n| List-I (Matrix Expression) | List-II (Determinant Value) | ||
|---|---|---|---|
| A | \( |A^2| \) | I | \( 4 \) |
| B | \( |\text{adj } A| \) | II | \( 16 \) |
| C | \( |\text{adj }(\text{adj } A)| \) | III | \( 8 \) |
| D | \( |2A| \) | IV | \( 16 \) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option B
A-(I), B-(I), C-(II), D-(II)
Explanation
\( |A^2| = |A|^2 = 4 \) (matches I). \( |\text{adj } A| = |A|^2 = 4 \) (matches I). \( |\text{adj }(\text{adj } A)| = |A|^4 = 16 \) (matches II). \( |2A| = 2^3 |A| = 16 \) (matches II).
