Question

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

• A. $8 \left[\begin{matrix}1&0&0\\\ 1&1&0\\\ 1&1&1\end{matrix}\right]$
• B. $12 \left[\begin{matrix}1&0&0\\\ 1&1&0\\\ 1&1&1\end{matrix}\right]$
• C. $16 \left[\begin{matrix}1&0&0\\\ 1&1&0\\\ 1&1&1\end{matrix}\right]$
• D. none of these

Answer 1

Answer: (C)

$16 \left[\begin{matrix}1&0&0\\\ 1&1&0\\\ 1&1&1\end{matrix}\right]$

Answer 2

We have, $A =\left[\begin{matrix}2&0&0\\\ 2&2&0\\\ 2&2&2\end{matrix}\right]$ $\therefore\quad adj \, A =\left[\begin{matrix}4&0&0\\\ -4&4&0\\\ 0&-4&4\end{matrix}\right]$ $\therefore\quad adj \,\left(adjA\right) =\left[\begin{matrix}16&0&0\\\ 16&16&0\\\ 16&16&16\end{matrix}\right]=16 \left[\begin{matrix}1&0&0\\\ 1&1&0\\\ 1&1&1\end{matrix}\right]$