Solution
= Solution
Put $c=\cos\theta$, $s=\sin\theta$. The <characteristic polynomial> is $(c-\lambda)^2-s^2$, giving
$$
\boxed{\lambda_+=c+s,\qquad\lambda_-=c-s.}
$$
When $s=0$, these <eigenvalues> coincide and $A=cI=\pm I$.
= Solution
Put $c=\cos\theta$, $s=\sin\theta$. The <characteristic polynomial> is $(c-\lambda)^2-s^2$, giving
$$
\boxed{\lambda_+=c+s,\qquad\lambda_-=c-s.}
$$
When $s=0$, these <eigenvalues> coincide and $A=cI=\pm I$.