Question

Given that A is a square matrix of order 3 and |A| = –2, then |adj(2A)| is equal to ______.

Options

• –2⁶

• +4

• –2⁸

• 2⁸

Answer 1

Given that A is a square matrix of order 3 and |A| = –2, then |adj(2A)| is equal to 2⁸.

Explanation:

|adj(2A)| = |(2A)|²

= (2³ |A|)²

= 2⁶ |A|²

= 2⁶ × (–2)²

= 2⁸.