Match List-I with List-II

List-I	List-II
(Matrix)	(Inverse of the Matrix)
(A) $\begin{pmatrix} 1 & 7 \\ 4 & -2 \end{pmatrix}$	(I) $\begin{pmatrix} 2/15 & 1/10 \\ -1/15 & 1/5 \end{pmatrix}$
(B) $\begin{pmatrix} 6 & -3 \\ 2 & 4 \end{pmatrix}$	(II) $\begin{pmatrix} 1/5 & -2/15 \\ -1/10 & 7/30 \end{pmatrix}$
(C) $\begin{pmatrix} 5 & 2 \\ -5 & 4 \end{pmatrix}$	(III) $\begin{pmatrix} 1/15 & 7/30 \\ 2/15 & -1/30 \end{pmatrix}$
(D) $\begin{pmatrix} 7 & 4 \\ 3 & 6 \end{pmatrix}$	(IV) $\begin{pmatrix} 2/15 & -1/15 \\ 1/6 & 1/6 \end{pmatrix}$

Choose the correct answer from the options given below:

For a 2×2 matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$, the inverse is:

$A^{-1} = \dfrac{1}{ad - bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}$

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For Matrix (A): $\begin{pmatrix} 1 & 7 \\ 4 & -2 \end{pmatrix}$

Determinant $= (1)(-2) - (7)(4) = -2 - 28 = -30$

$A^{-1} = \dfrac{1}{-30}\begin{pmatrix} -2 & -7 \\ -4 & 1 \end{pmatrix}$

$= \begin{pmatrix} 2/30 & 7/30 \\ 4/30 & -1/30 \end{pmatrix}$

$= \begin{pmatrix} 1/15 & 7/30 \\ 2/15 & -1/30 \end{pmatrix}$

This matches (III)

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For Matrix (B): $\begin{pmatrix} 6 & -3 \\ 2 & 4 \end{pmatrix}$

Determinant $= (6)(4) - (-3)(2) = 24 + 6 = 30$

$B^{-1} = \dfrac{1}{30}\begin{pmatrix} 4 & 3 \\ -2 & 6 \end{pmatrix}$

$= \begin{pmatrix} 4/30 & 3/30 \\ -2/30 & 6/30 \end{pmatrix}$

$= \begin{pmatrix} 2/15 & 1/10 \\ -1/15 & 1/5 \end{pmatrix}$

This matches (I)

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For Matrix (C): $\begin{pmatrix} 5 & 2 \\ -5 & 4 \end{pmatrix}$

Determinant $= (5)(4) - (2)(-5) = 20 + 10 = 30$

$C^{-1} = \dfrac{1}{30}\begin{pmatrix} 4 & -2 \\ 5 & 5 \end{pmatrix}$

$= \begin{pmatrix} 4/30 & -2/30 \\ 5/30 & 5/30 \end{pmatrix}$

$= \begin{pmatrix} 2/15 & -1/15 \\ 1/6 & 1/6 \end{pmatrix}$

This matches (IV)

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For Matrix (D): $\begin{pmatrix} 7 & 4 \\ 3 & 6 \end{pmatrix}$

Determinant $= (7)(6) - (4)(3) = 42 - 12 = 30$

$D^{-1} = \dfrac{1}{30}\begin{pmatrix} 6 & -4 \\ -3 & 7 \end{pmatrix}$

$= \begin{pmatrix} 6/30 & -4/30 \\ -3/30 & 7/30 \end{pmatrix}$

$= \begin{pmatrix} 1/5 & -2/15 \\ -1/10 & 7/30 \end{pmatrix}$

This matches (II)

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List-I	List-II
(A)	→ (III)
(B)	→ (I)
(C)	→ (IV)
(D)	→ (II)

Therefore, the correct answer is (A)-(III), (B)-(I), (C)-(IV), (D)-(II).