Match List-I with List-II

List-I	List-II
(Matrix)	(Determinant)
(A) $\begin{bmatrix} 1 & 7 \\ -3 & 5 \end{bmatrix}$	(I) 24
(B) $\begin{bmatrix} -2 & 5 \\ -3 & -3 \end{bmatrix}$	(II) 32
(C) $\begin{bmatrix} -12 & 8 \\ -16 & 8 \end{bmatrix}$	(III) 21
(D) $\begin{bmatrix} 15 & 9 \\ -21 & -11 \end{bmatrix}$	(IV) 26

Choose the correct answer from the options given below:

For any 2×2 matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, the determinant is:

Determinant $= (a × d) - (b × c)$

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For $\begin{bmatrix} 1 & 7 \\ -3 & 5 \end{bmatrix}$:

Main diagonal: $1 × 5 = 5$

Other diagonal: $7 × (-3) = -21$

Determinant $= 5 - (-21)$

$= 5 + 21$

$= 26$

A matches with (IV)

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For $\begin{bmatrix} -2 & 5 \\ -3 & -3 \end{bmatrix}$:

Main diagonal: $(-2) × (-3) = 6$

Other diagonal: $5 × (-3) = -15$

Determinant $= 6 - (-15)$

$= 6 + 15$

$= 21$

B matches with (III)

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For $\begin{bmatrix} -12 & 8 \\ -16 & 8 \end{bmatrix}$:

Main diagonal: $(-12) × 8 = -96$

Other diagonal: $8 × (-16) = -128$

Determinant $= -96 - (-128)$

$= -96 + 128$

$= 32$

C matches with (II)

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For $\begin{bmatrix} 15 & 9 \\ -21 & -11 \end{bmatrix}$:

Main diagonal: $15 × (-11) = -165$

Other diagonal: $9 × (-21) = -189$

Determinant $= -165 - (-189)$

$= -165 + 189$

$= 24$

D matches with (I)

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Therefore, the correct matching is:

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