Question

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

• A. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

Answer: (A)

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