If A is a square matrix of order 3 such that $|A|= 3$, then $|adj(adj\, A)|$ is equal to:

81

The correct answer is Option (4) → 81

Given: $A$ is a $3 \times 3$ matrix and $|A| = 3$.

For an $n \times n$ matrix:

$|\text{adj}\,A| = |A|^{\,n-1}$

Since $n = 3$:

$|\text{adj}\,A| = 3^{2} = 9$

Now apply the formula again to $\text{adj}\,A$ (which is also $3 \times 3$):

$|\text{adj}(\text{adj}\,A)| = |\text{adj}\,A|^{\,n-1}$

$= 9^{2}$

$= 81$

Thus, $|\text{adj}(\text{adj}\,A)| = 81$.