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Let A be a 3 × 3 invertible matrix. If adj 24 A = adj 3 adj 2 A | , then A 2 is equal to

Options

  1. A2 6
  2. B2 12
  3. C512
  4. D6 6

Correct answer

A. 2 6

Step-by-step solution

We know that adj A = A n - 1 K A = K n A where n is order of matrix Given adj 24 A = adj 3 adj 2 A ⇒ 24 A 2 = 3 adj 2 A 2 ⇒ 24 A = 3 adj 2 A ⇒ 24 3 A = 3 3 adj 2 A ⇒ 24 3 A = 3 3 2 A 2 A ⇒ 24 3 A = 3 3 2 3 2 3 A A ⇒ A = 24 3 2 3 2 3 3 3 = 2 3 · 3 3 2 6 3 3 = 8 ⇒ A 2 = 64

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