Question

If A = $\left[\begin{array}{cc}4& 2\\ 5& 3\end{array}\right]$ then $|adj\left(adjA\right)|=$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

We know if $A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$

Then, $adj\left(A\right)=\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$

We have, $A=\left[\begin{array}{cc}4& 2\\ 5& 3\end{array}\right]$

Then, $adj\left(A\right)=\left[\begin{array}{cc}3& -2\\ -5& 4\end{array}\right]$

and, $\left[adj\right(adjA\left)\right]=\left[\begin{array}{cc}4& 2\\ 5& 3\end{array}\right]$

$\therefore |adj\left(adjA\right)|=\left(\begin{array}{cc}4& 2\\ 5& 3\end{array}\right)$

$=4\times 3-2\times 5$

$=12-10$

$=2$

So, Correct option is $\text{B}$.