If $A =\begin{bmatrix}\cos θ&-\sin θ\\\sin θ&\cos θ\end{bmatrix}$, then $A^T+A=I_2$, if
Answer & explanation
Correct answer: option 3
We have,
$A^T+A=I_2$
$⇒\begin{bmatrix}\cos θ&\sin θ\\-\sin θ&\cos θ\end{bmatrix}+\begin{bmatrix}\cos θ&-\sin θ\\\sin θ&\cos θ\end{bmatrix}=\begin{bmatrix}1&0\\0&1\end{bmatrix}$
$⇒\cos θ=\frac{1}{2}=\cos \frac{п}{3}⇒θ=2nп±\frac{п}{3},n∈Z$