Question

Let A be a matrix of order 3×3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to ______.

• A. $512 × 10^6$
• B. $256 × 10^6$
• C. $1024 × 10^6$
• D. $256 × 10^{11}$

Answer 1

Answer: (A)

$512 × 10^6$

Answer 2

|A| = 2
||A| adj(5 adjA3)|
= |25|A| adj(adjA3)|
= 253 |A|3⋅ |adjA3|2
= 253⋅ 23⋅ |A3|4
= 253⋅ 23⋅ 212
= 106⋅ 512
= 512⋅106

So, the correct option is (A): 512 x 106