Question

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4$ Then $\mid A ^{-1}$ adj $A \mid$ is equal to

• A. 1
• B. $\sqrt{6}$
• C. 12
• D. $2 \sqrt{3}$

Answer 1

Answer: (D)

$2 \sqrt{3}$

Answer 2

The correct answer is (D) : $2 \sqrt{3}$
Given ∣adj(adj(adj.A))∣=124 ⇒∣A∣(n−1)3=124
Given n=3
⇒∣A∣8=124
⇒∣A∣2=12
∣A∣=23​
We are asked
∣∣​A−1⋅adjA∣∣​
=∣∣​A−1∣∣​⋅∣adjA∣
=∣A∣1​⋅∣A∣3−1
=∣A∣=23​