Reason behind the uncertainty principle

Question

I know that Heisenberg Uncertainty principles states that the momentum and position of a quantum object can not be determined at the same time. This is very strange to me. I want the basic reason behind it, i.e why is this so.

Answer 1

The basic reason is that the position operator X and the momentum operator P cannot be simultaneously diagonalized because $[X,P]=i\hbar I\ne{0}$. This means there is no state which is simultaneously an eigenstate of both X and P.