Match List-I with List-II

Choose the correct answer from the options given below:

(A)-(IV), (B)-(III), (C)-(II), (D)-(I)

The correct answer is Option (4) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)

Given: Determinant of adj(A) for a 2×2 matrix is given by:

$\det(\text{adj}(A)) = (\det(A))^{n-1}, \; n=2 \;\;\Rightarrow\;\; \det(\text{adj}(A)) = \det(A)$

Now, compute determinants:

(A) $A=\begin{bmatrix}3 & 1 \\ 4 & 2\end{bmatrix}, \;\det(A)=3(2)-1(4)=6-4=2$ $\;\;\Rightarrow \det(\text{adj}(A))=2$

(B) $A=\begin{bmatrix}5 & -1 \\ 4 & 2\end{bmatrix}, \;\det(A)=5(2)-(-1)(4)=10+4=14$ $\;\;\Rightarrow \det(\text{adj}(A))=14$

(C) $A=\begin{bmatrix}6 & -1 \\ 2 & 1\end{bmatrix}, \;\det(A)=6(1)-(-1)(2)=6+2=8$ $\;\;\Rightarrow \det(\text{adj}(A))=8$

(D) $A=\begin{bmatrix}4 & 1 \\ 3 & 3\end{bmatrix}, \;\det(A)=4(3)-1(3)=12-3=9$ $\;\;\Rightarrow \det(\text{adj}(A))=9$