Let A be a non singular matrix of order n × n, Then |adj (3A)| is equal to:
Answer & explanation
Correct answer: option 2
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, $|adj(3A)| = (3^n |A|)^(n-1) = 3^{n(n-1)} |A|^{n-1}$