Question

Let A be a 3 × 3 invertible matrix. If |adj (24A)| = |adj (3 adj (2A))|, then |A|2 is equal to :

• A. 66
• B. 212
• C. 26
• D. 1

Answer 1

Answer: (A)

66

Answer 2

The correct answer is (C) : 26
$|adj(24A)|=|adj(3adj(24A))|$
$⇒ |24A|^2=|3adj(2A)|^2$
$⇒(24^3)^2⋅|A|^2=(3^3)^2|adj(2A)|^2$
$⇒24^6⋅|A|^2=3^6|2A|^4$
$⇒24^6|A|^2=3^6⋅(2^3)^4|A|^4$
$⇒|A|^2=\frac{24^6}{3^6.2^{12}}=\frac{2^{18}.3^6}{3^6.2^{12}}=2^6$