alleryIf $A$ is a square matrix with $|A| = 3$ and order $n = 3$, then $|\operatorname{adj}(A)|$ equals:
A$3$
B$9$
C$27$
D$1/3$
Answer & Solution
Correct answer: B. $9$
$|\operatorname{adj}(A)| = |A|^{n - 1}$.
With $|A| = 3$ and $n = 3$, this gives $|\operatorname{adj}(A)| = 3^{3 - 1} = 3^2 = 9$.
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