Let A be a non singular matrix of order n × n, Then |adj (3A)| is equal to:

$3^{n(n-1)}|A|^{n-1}$

The correct answer is Option (2) → $3^{n(n-1)}|A|^{n-1}$

Given: A is a non-singular matrix of order n × n

Property: $|adj(B)| = |B|^(n-1)$ for a square matrix B of order n

Here,$ B = 3A ⇒ |adj(3A)| = |3A|^(n-1)$

Also, $|3A| = 3^n |A|$

Therefore, $|adj(3A)| = (3^n |A|)^(n-1) = 3^{n(n-1)} |A|^{n-1}$