If \( \mathrm{A} \) is a square matrix of order 3, then
Match List-I with List-II
| List-I | List-II | ||
| \( |\mathrm{A}| = \) | \( |\mathrm{adj}\,\mathrm{A}| = \) | ||
| (A) | 4 | (I) | 16 |
| (B) | 3 | (II) | 9 |
| (C) | 2 | (III) | 4 |
| (D) | 1 | (IV) | 1 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
For a square matrix of order n, \( |\mathrm{adj}\,\mathrm{A}|=|\mathrm{A}|^{n-1} \). Here n = 3, so
\( \displaystyle |\mathrm{adj}\,\mathrm{A}|=|\mathrm{A}|^{2} \)
(A) \( |\mathrm{A}|=4 \) → \( 4^{2}=16 \), which is (I)
(B) \( |\mathrm{A}|=3 \) → \( 3^{2}=9 \), which is (II)
(C) \( |\mathrm{A}|=2 \) → \( 2^{2}=4 \), which is (III)
(D) \( |\mathrm{A}|=1 \) → \( 1^{2}=1 \), which is (IV)
So the matching is (A) - (I), (B) - (II), (C) - (III), (D) - (IV).
NCERT Exemplar:
Determinants
