Discussion
Let A be a square matrix of order 3 and \(|A| = 9\) Then \(|adj(adjA)| =\)
Answer: A
\(|adj(adj A)|\) equals 6561.
For a square matrix of order n, \(|adj A| = |A|^{n-1}\), so applying it twice gives
\[ |adj(adj A)| = |A|^{(n-1)^{2}} = 9^{4} = 6561 \]
for \(n = 3\). Using \(|A|^{n-1}\) only once would give 81. The other options are near-misses of \(9^{4}\) that come from no rule.
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