Question

If $A=\left[\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right]$ and $A\cdot adj\left(A\right)=k\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ then $k$ is

• A. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

Answer: (A)

$\left[\begin{array}{cc}cos\theta & sin\theta \\ -sin\theta & cos\theta \end{array}\right]\left[\begin{array}{cc}cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}\right]=\left|A\right|I$
$A(adjA)=\left|A\right|Ihere\left|A\right|=1$
$\Rightarrow K=1$