Question

Let $n\ge 2$ be an integer.
$A=\left[\begin{array}{ccc}\cos \left(\frac{2\pi }{n}\right)& \sin \left(\frac{2\pi }{n}\right)& 0\\ -\sin \left(\frac{2\pi }{n}\right)& \sin \left(\frac{2\pi }{n}\right)& 0\\ 0& 0& 1\end{array}\right]$ and $I$ is the identify matrix of order $3$., then following of which is correct

• A. $A^n+I$ and $A^{n-1}\ne I$
• B. $A^m\ne I$ for any positive integer $m$
• C. $A$ is not invertible
• D. $A$ is invertible

Answer 1

The correct option is A $A^n+I$ and $A^{n-1}\ne I$