Match List-I with List-II
| List-I | List-II |
| Matrix A | |adjA| |
| (A) \( \begin{bmatrix}2 & 1\\3 & 4\end{bmatrix} \) | (I) 2 |
| (B) \( \begin{bmatrix}3 & 0\\1 & 5\end{bmatrix} \) | (II) 5 |
| (C) \( \begin{bmatrix}6 & -1\\5 & 3\end{bmatrix} \) | (III) 15 |
| (D) \( \begin{bmatrix}1 & 0\\0 & 2\end{bmatrix} \) | (IV) 23 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
For a 2 × 2 matrix, \( |\mathrm{adj}\,A|=|A|^{2-1}=|A| \), so each value is just the determinant.
(A) \( \begin{bmatrix}2 & 1\\3 & 4\end{bmatrix} \)
This matches (II) 5.
\( 8-3=5 \)
(B) \( \begin{bmatrix}3 & 0\\1 & 5\end{bmatrix} \)
This matches (III) 15.
\( 15-0=15 \)
(C) \( \begin{bmatrix}6 & -1\\5 & 3\end{bmatrix} \)
This matches (IV) 23.
\( 18-(-5)=23 \)
(D) \( \begin{bmatrix}1 & 0\\0 & 2\end{bmatrix} \)
This matches (I) 2.
\( 2-0=2 \)
So the matching is (A) - (II), (B) - (III), (C) - (IV), (D) - (I).