Let α β  = 0 and A = β α − β α α α 3 β 2 α . If B = 3 α − α − 2 α − 9 7 5 3 α − 2 α − 2 β is the matrix of cofactors of the elements of A , then det ( A B ) is equal to :

Question

Let α β  = 0 and A = ​ β α − β ​ α α α ​ 3 β 2 α ​ ​ . If B = ​ 3 α − α − 2 α ​ − 9 7 5 ​ 3 α − 2 α − 2 β ​ ​ is the matrix of cofactors of the elements of A , then det ( A B ) is equal to :

TestHub · Accepted Answer

Equating co-factor fo A 21 ​ ​ ( 2 α 2 − 3 α ) = α α = 0 , 2 (accept) ​ Now, 2 α 2 − α β = 3 α ​ α = 2 β = 1 ∣ AB ∣ = ∣ A cof ( A ) ∣ = ∣ A ∣ 3 A = ​ 1 2 − 1 ​ 2 2 2 ​ 3 1 4 ​ ​ = 6 − 2 ( 9 ) + 3 ( 6 ) = 6 ​

Mathematics - Matrices Question with Solution | TestHub

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