If A be a square matrix of order 3 such that $|A| = 2$, then $|adj (2A)|$ is equal to

256

The correct answer is Option (4) → 256

Given: $|A| = 2$, and $A$ is a $3 \times 3$ matrix.

Formula: $|kA| = k^n |A|$, where $n$ is the order of the matrix.

So, $|2A| = 2^3 |A| = 8 \times 2 = 16$

Also, for any square matrix $A$ of order $n$, $|adj(A)| = |A|^{n-1}$

Hence, $|adj(2A)| = |2A|^{3-1} = (16)^2 = 256$

Final Answer:

$|adj(2A)| = 256$