Mathematics - Matrices Question with Solution | TestHub

Given equation is

$\left|adj\left(adj\left(adj.A\right)\right)\right|={12}^4$

$\Rightarrow {\left|A\right|}^{(n-1{)}^3}={12}^4$

$\because n=3$

$\Rightarrow {\left|A\right|}^{(3-1{)}^3}={12}^4$

$\Rightarrow {\left|A\right|}^8={12}^4$

$\Rightarrow {\left|A\right|}^2=12$

$\Rightarrow \left|A\right|=2\sqrt{3}$

Now, $\left|A^{-1}adj A\right|=\left|A^{-1}\right|.\left|adj A\right|=\frac{1}{\left|A\right|}\times {\left|A\right|}^{3-1}$

$=\left|A\right|=2\sqrt{3}$