An ideal op-amp has infinite differential gain, infinite input impedance, infinite bandwidth, zero output impedance, zero common mode gain, and so forth.
Consequently the common mode input voltage can be anything and the differential input voltage will be zero.
If you find one it will likely be expensive.
1. The purpose is to amplify the to maximize the open loop gain, which is the gain without considering the feedback. And to create an ideal op-amp this factor has to be infinite.
2. Input impedance is infinite. Hence, input current passed = 0
3.Output impedance is assumed to be zero acting as a perfect internal voltage source with no internal resistance so that it can supply as much current as necessary to the load.
4. The amplifiers output will be zero when the voltage difference between the inverting and the non-inverting inputs is zero, the same or when both inputs are grounded.
The above characteristics of an ideal op-amp lead us to an op-amp with
input resistance is infinite, so no current flows into either input terminal (the “current rule”) and that the differential input offset voltage is zero (the “voltage rule”). – which forms a voltage controlled voltage source!