Why is the voltage across the inputs of an ideal OP Amp zero?
You misunderstood the "axiom" 

An Ideal opamp will do what it can to make the differential voltage between the -ve pin and the +ve pin equal zero. It doesn't state it is zero 

All it can do is alter its output and thus with negative feedback there OPAMP stands a chance of making the difference zero

You then make use of that fact during circuit analysis to simplify calculations "if the difference is zero and the +ve terminal is at 0V, then the output must be...)