Question:

If $A$ is $3\times3$ and $|A|=2$, then $\left|3\,\text{adj}(|3A|A^2)\right|$ is equal to

$3^{12}\cdot6^{11}$

$3^{12}\cdot6^{10}$

$3^{10}\cdot6^{11}$

$3^{11}\cdot6^{10}$

Step-by-Step Solution

Key Concept: $|3A|=3^3\cdot2=54$. $|\text{adj}(kA^2)|=(k)^{(n-1)^2}|\text{adj}(A^2)|$... use $|\text{adj}(B)|=|B|^{n-1}$ and $|kB|=k^n|B|$.

$3^{11}\cdot6^{10}$.

Correct Answer: 4