Question

If A is a square matrix of order 3 and |A| = –5, then |adj A| is ______.

Options

• 125

• –25

• 25

• ±25

Answer 1

If A is a square matrix of order 3 and |A| = –5, then |adj A| is 25.

Explanation:

Since, |adj A| = |A|^{n – 1}

Where n is the order of the matrix

∴ |adj A| = (–5)^{3 – 1}

= 5²

= 25