Let ∈ (0 , ) and A= (12 101012 ). If det ⁡( adj ⁡(2A-A^T) adj ⁡(A-2A^T))=2^8, then ( det ⁡ (A ) )^2 is equal to:

Question

Accepted Answer

Correct answer: B. (b) ( adj ⁡(A-2 A^T)(2 A-A^T) )=28 (( A-2 A^T)(2 A-A^T) )=24( A-2 A^T)(2 A-A^T)= 16( A-2 A^T)^T=A^T-2 A( A-2 A^T)=(A^T-2 A) ⇒(A-2 A^T)^2=16( A-2 A^T)= 4 (12 101012 )- (2204022 24 ) (-10 -30-1-2 -1-2)1+3 =43 =3 =1 | A |= (121101012 )=-1-3=-4 |A |^2=16

$Let α \in (0, \infty) and A = (12 α 101012) . If det (adj (2 A - A^{T}) \cdot adj (A - 2 A^{T})) = 2^{8}, then (det (A))^{2} is equal to:$

Solution

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