If and det (A³) = 125, then α is equal to

Question

Question

This question was previously asked in

NDA (Held On: 23 April 2017) Maths Previous Year paper

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Answer 1

Concept:

1. If then determinant of A is given by: |A| = a₁₁ × a₂₂ – a₂₁ × a₁₂

2. |Aⁿ| = |A|ⁿ

Calculation:

Given that,

and det{A³} = 125

⇒ |A| = α × α – 2 × 2

⇒ |A| = α² - 4 ...1)

Given |A³| = 125

⇒ |A|³ = 125 ...[∵ |Aⁿ| = |A|ⁿ]

⇒ |A| = (125)^1/3 = 5 ...2)

From equations 1 and 2

⇒ α² - 4 = 5

⇒ α² = 9

⇒ α = ± 3