Question

Let A and B be two $3 × 3$ matrices such that AB = I and |A| =$\frac{1}{8}$. Then |adj (B adj(2A))| is equal to

• A. 16
• B. 32
• C. 64
• D. 128

Answer 1

Answer: (C)

64

Answer 2

A and B are two matrices of order $3×3$.

and AB = I, |A|=$\frac{1}{8}$

Now, |A||B|=$1$

|B|=$8$

∴$|adj(B(adj(2A))|$

$= |B(adj(2A))|^2$

= $|B|^2|adj(2A)|^2 = 2^6|2A|^{2×2 }$

=$2^ 6.2^{ 12}.\frac{1}{2 ^{12}}=64$