Question

If $A$ and $B$ are two matrices of same order $3\times 3$, where
$A=\left[\begin{array}{ccc}1& 2& 3\\ 2& 3& 4\\ 5& 6& 8\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& 2& 5\\ 2& 3& 8\\ 7& 2& 9\end{array}\right]$

The value of $\text{Adj}\left(\text{Adj}A\right)$ is equal to

• A. $-A$
• B. $A$
• C. $8A$
• D. $16A$

Answer 1

Answer: (A)

$-A$

$\left|A\right|=1(3\times 8-4\times 6)-2(2\times 8-5\times 4)+3(2\times 6-5\times 3)=-1$
Use following results
$\text{Adj}\left(\text{Adj}A\right)={\left|A\right|}^{n-2}A\Rightarrow \text{Adj}\left(\text{Adj}A\right)={\left|A\right|}^{n-2}A={(-1)}^{1}A=-A$
Ans: $A$