Question

If $A=\left[\begin{array}{cc}\cos x& \sin x\\ -\sin x& \cos x\end{array}\right]$ and $AadjA=k\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ then the value of $k$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

Answer: (B)

$1$

We know that,
$A\left(adjA\right)=|A|I$
Given, $A=\left[\begin{array}{cc}\cos x& \sin x\\ -\sin x& \cos x\end{array}\right]$
$|A|={\cos }^{2}x+{\sin }^{2}x=1$
$|A|={\cos }^{2}x+{\sin }^{2}x=1$
$\therefore A\left(adjA\right)=1\cdot I=kI$
$k=1$.