Question

Let A be nonsingular square matrix of order 3 × 3 Then |adj A| is equal to.

Options

• |A|

• |A|²

• |A|³

• 3|A|

Answer 1

|A|² 

Explanation:

(adj A) = A = |A|I

= `[(|A|, 0, 0),(0, |A|, 0),(0, 0, |A|)]`

⇒ |(adj A)A| = `[(|A|, 0, 0),(0, |A|, 0),(0, 0, |A|)]`

⇒ |adj A| |A| = |A|³

= `|(1, 0, 0),(0, 1, 0),(0, 0, 1)| |A|^2 (1)`

∴ |adj A| = |A|²