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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Matrices

Question:

If A and B are invertible matrices of order 3 then match List-I with List-II

List-I

List-II

(A) $\text{adj(A)}$

(I) $B^{-1} A^{-1}$

(B) $(AB)^{-1}$

(II) $|A|^{-1}$

(C) $|A^{-1}|$

(III) $|A|^2$

(D) $\text{|adj A|}$

(IV) $|A|A^{-1}$

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

The correct answer is Option (3) → (A)-(IV), (B)-(I), (C)-(II), (D)-(III)

List-I

List-II

(A) $\text{adj(A)}$

(IV) $|A|A^{-1}$

(B) $(AB)^{-1}$

(I) $B^{-1} A^{-1}$

(C) $|A^{-1}|$

(II) $|A|^{-1}$

(D) $\text{|adj A|}$

(III) $|A|^2$

Given: A and B are invertible matrices of order 3.

Key identities:

1. adj(A) = |A| A⁻¹

2. (AB)⁻¹ = B⁻¹ A⁻¹

3. |A⁻¹| = 1 / |A|

4. |adj A| = |A|² (since order = 3, so (n−1) = 2)

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