Mathematics - Matrices Question with Solution | TestHub

$\because A^{-1}=\frac{1}{\left|A\right|}\left(adj\left(A\right)\right)$

$\therefore adj\left(adjA\right)=\left|adj A\right|{\left(adj A\right)}^{-1}={\left|A\right|}^2{\left(adj A\right)}^{-1}\dots \dots \left(\mathrm{i}\right)$

$\because A\left(adj A\right)=\left|A\right|\mathrm{I}$

$\therefore adj\left(A\right)=\left|A\right|A^{-1}$

$\therefore {\left(adj A\right)}^{-1}=\frac{1}{\left|A\right|}A$

$\therefore$$\mathrm{ from\; (i)}$

$adj\left(adj A\right)=\left|A\right|.A$