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  4. If A = [ beginmatrix2&0&0 2&2&0 2&2&2 endmatrix], then adj (adj A) is equal to

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Q. If $A = \left[\begin{matrix}2&0&0\\ 2&2&0\\ 2&2&2\end{matrix}\right]$, then adj (adj A) is equal to

Determinants

Solution:

We have, $A =\left[\begin{matrix}2&0&0\\ 2&2&0\\ 2&2&2\end{matrix}\right]$

$\therefore \quad adj \, A =\left[\begin{matrix}4&0&0\\ -4&4&0\\ 0&-4&4\end{matrix}\right]$

$\therefore \quad adj \,\left(adjA\right) =\left[\begin{matrix}16&0&0\\ 16&16&0\\ 16&16&16\end{matrix}\right]=16 \left[\begin{matrix}1&0&0\\ 1&1&0\\ 1&1&1\end{matrix}\right]$