If A is square matrix of order 3 × 3 and $\text{|adj A| = 64}$, then the value of $|5A|$ is

±1000

The correct answer is Option (2) → ±1000

Given:

$| \text{adj } A | = 64$

$A$ is a $3 \times 3$ matrix

Property: If $A$ is a square matrix of order $n$ and $\det(A) \ne 0$, then

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

Here, $n = 3$, so:

$|\text{adj } A| = |\det A|^{2} = 64 \Rightarrow |\det A| = \sqrt{64} = 8$

Now, compute $|5A|$:

$|kA| = k^n |A|$ for an $n \times n$ matrix

$\Rightarrow |5A| = 5^3 \cdot |A| = 125 \cdot 8 = {1000}$