You need to understand what A is here. A here is a rotation Matrix which rotates any vector by pi/2 (90 degrees).
Once you observe this, you can see the correct option directly without any calculations. I am giving the thought process below :
You can see that A^4 - I = 0 and A^2 + I = 0. Hence, Option 2.
(Linear Algebra is best understood with pictures and coordinate geometry, they are one or the same thing. )