Match List-I with List-II
| List-I | List-II |
| A is given matrix | |adj (adjA)| |
| (A) Order of A = 2 x 2 and |A| = 3 | (I) 3 |
| (B) Order of A = 3 x 3 and |A| = 2 | (II) 1 |
| (C) Order of A = 4 x 4 and |A| = 1 | (III) 16 |
| (D) Order of A = 2 x 2 and |A| = 4 | (IV) 4 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
For a square matrix of order n,
\( |\mathrm{adj}(\mathrm{adj}\,A)|=|A|^{(n-1)^2} \)
(A) Order of A = 2 x 2 and |A| = 3
This matches (I) 3.
\( 3^{(2-1)^2}=3^1=3 \)
(B) Order of A = 3 x 3 and |A| = 2
This matches (III) 16.
\( 2^{(3-1)^2}=2^4=16 \)
(C) Order of A = 4 x 4 and |A| = 1
This matches (II) 1.
\( 1^{(4-1)^2}=1 \)
(D) Order of A = 2 x 2 and |A| = 4
This matches (IV) 4.
\( 4^{(2-1)^2}=4 \)
So the matching is (A) - (I), (B) - (III), (C) - (II), (D) - (IV).