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Home Questions 8FNF5JVQ5B
Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Algebra

Question:

Match List-I with List-II

List-I

List-II

(A) If A is a non-singular matrix of order n, then $\text{|A (adj A)|}$ is equal to

(I) $|A|^{n-1}$

(B) If A is a non-singular matrix of order n, then $\text{|adj (adj A)|}$ is equal to

(II) $|A|^{n-2}A$

(C) If A is a non-singular matrix of order n, then $\text{adj (adj A)}$ is equal to

(III) $|A|^n$

(D) If A is a non-singular matrix of order n, then $\text{|(adj A)|}$ is equal to

(IV) $|A|^{(n-2)^2}$

Choose the correct answer from the options given below:

Options:

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

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

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

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

Correct Answer:

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

Explanation:

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

*****

Matching and Explanation

(A) |A (adj A)|

We know:   A · adj(A) = |A| In

⟹ |A · adj(A)| = | |A| In | = |A|n

So, (A) → (III)

(C) adj(adj A)

For a non-singular matrix A of order n:

adj(adj A) = |A|n−2 A

So, (C) → (II)

(B) |adj(adj A)|

Taking determinants on both sides of (C):

|adj(adj A)| = | |A|n−2 A |

= |A|(n−2)n · |A|

= |A|(n−2)²

So, (B) → (IV)

(D) |adj A|

We know: |adj A| = |A|n−1

So, (D) → (I)

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