If A is a non – singular matrix of size$3\times 3$ , then adj (adj A) is equal to

As A is a non – singular matrix  $A^{-1}=\frac{1}{\left|A\right|}\left(adjA\right)$

$\Rightarrow adjA=\left|A\right|A^{-1}=B\left(say\right)$ .

Now, adj (adj A) = adj (B) = $\left|B\right|B^{-1}$

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

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

[using scalar multiple property of determinants ]

$={\left|A\right|}^3\frac{1}{\left|A\right|}.\frac{1}{\left|A\right|}A=\left|A\right|A$