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If A is a square matrix of order 5 and 9A^{-1}=4A^T then |adj

Question

If A is a square matrix of order 5 and $9 A^{- 1} = 4 A^{T}$ then |adj (adj (adj A))I (where $A^{- T}$ and adj(A) denotes the inverse, transpose and adjoint of matrix A respectively) contains: $(l o g 3 = 0.477, l o g 2 = 0.303)$

56 digits

60 digits

58 digits

53 digits

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Levi Discussed

If A is a square matrix of order 5 and

9 A^{- 1} = 4 A^{T}

then |adj (adj (adj A))I (where

A^{- T}

and adj(A) denotes the inverse, transpose and adjoint of matrix A respectively) contains:

(l o g 3 = 0.477, l o g 2 = 0.303)

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Text solutionVerified

9 A^{- 1} = 4 A^{T} \Rightarrow ∣9 A^{- 1} ∣ = ∣4 A^{T} ∣ \Rightarrow 9^{5} \times \frac{1}{∣ A ∣} = 4^{5} ∣ A ∣ \Rightarrow ∣ A ∣ = (\frac{3}{2})^{5}

|adj adj adj A|

= ∣ A ∣^{4^{3}} = (\frac{3}{2})^{320}

No. of digits in |adj adj adj A|

= [l o g (\frac{3}{2})^{320}] + 1 = 56

. ([.] denotes greatest integer function).

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Question Text	If A is a square matrix of order 5 and $9 A^{- 1} = 4 A^{T}$ then \|adj (adj (adj A))I (where $A^{- T}$ and adj(A) denotes the inverse, transpose and adjoint of matrix A respectively) contains: $(l o g 3 = 0.477, l o g 2 = 0.303)$
Answer Type	Text solution:1
Upvotes	150