If A is a square matrix of order 3, then | Adj(Adj A2)

Engineering

Mathematics

Introduction to Determinants

Question

If A is a square matrix of order 3, then | Adj(Adj A²) | =

|A|²

|A|⁴

|A|⁸

|A|¹⁶

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Order of A = 3 × 3

⇒ |Adj⁡(Adj⁡A²)) = |A²|⁽ⁿ^–¹⁾²
[∵ |adj⁡(adj⁡A)| = |A|(n-1)2

⇒ |A²|^{(3 – 1}⁾² = |A²|⁴ = |A|⁸

Ans - Option ' C '

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