Question

A= $\left[\begin{array}{ccc}3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right]$ ,then Adj ( A)

• A. 3A
• B. 6A
• C. $9A^T$
• D. $2A^T$

Answer 1

The correct option is A 3A

We have, $A=\left[\begin{array}{ccc}3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right]$
co-factor matrix of $A$ is,
$B=\left[\begin{array}{ccc}9& 0& 0\\ 0& 9& 0\\ 0& 0& 9\end{array}\right]$
Thus
$\therefore$ Adj(A)$=B^T=\left[\begin{array}{ccc}9& 0& 0\\ 0& 9& 0\\ 0& 0& 9\end{array}\right]=3\left[\begin{array}{ccc}3& 0& 0\\ 0& 3& 0\\ 0& 0& 3\end{array}\right]=3A$