Question

If A is non-singular matrix of order 3 × 3, then adj (adj A) is equal to –

• A. |A| A
• B. |A|² A
• C. |A|^–1 A
• D. None of these

Answer 1

Answer: (A)

|A| A

Answer 2

As A is a non-singular matrix A^–1 = $\frac{1}{|A|}$ (adj A)

Ž adj A = |A| A^–1 = B(say).

Now,

adj (adj A) = adj (2) = |B|B^–1 = ||A|A^–1| (|A| A^–1)^–1

= |A|³ |A^–1| |A|^–1 (A^–1)^–1

[using scalar multiple property of determinants]

= |A|³ $\frac{1}{|A|}$· $\frac{1}{|A|}$A = |A| A.