Let A and B be two 3 [] 3 matrices such that AB = I and [|A| = 1 8].

Question

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

Accepted Answer

A and B are two matrices of order 3 $$\times$$ 3.

and $AB = I$,

$$|A| = {1 \over 8}$$

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

$|B| = 8$

$$\therefore$$ $|adj(B(adj(2A))| = |B(adj(2A)){|^2}$

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

$$ = {2^6}|2A{|^{2 \times 2}}$$

$$ = {2^6}.\,{2^{12}}.\,{1 \over {{2^{12}}}} = 64$$

Solutions · 1