Let A be 3 x 3 matrix such that det(A) = 5. If det(3 adj(2A adj(2A))) = a^α . 3^β . 5^γ,

Question

Let A be \(3 \times 3\) matrix such that \(\operatorname{det}(A)=5.\) If \(\operatorname{det}(3 \operatorname{adj}(2 A \operatorname{adj}(2 A)))=2^{\alpha} \cdot 3^{\beta} \cdot 5^{\gamma},\) then \((\alpha+\beta+\gamma)\) is equal to

(1) 25

(2) 26

(3) 27

(4) 28

Answer 1

Correct option is: (3) 27  

\( \Rightarrow \alpha=18 \)

\( \beta=3 \)

\( \gamma=6 \)

\( \Rightarrow \alpha+\beta+\gamma=27\)