An ideal operational amplifier (op-amp) is defined by the following properties:
1. Infinite input resistance: This means that the current into the input terminals of the op-amp is zero. Therefore, the ideal op-amp has infinite input resistance, which is why Option (A) is true.
2. Zero output resistance: An ideal op-amp has zero output resistance, not infinite output resistance, which makes Option (B) false.
3. Infinite open-loop differential gain: The ideal op-amp has an infinite gain when the differential input is applied. Thus, Option (C) is true.
4. Zero open-loop common-mode gain: In the ideal op-amp, the common-mode gain is zero, not infinite. Hence, Option (D) is false.
Thus, the correct answer is (A) and (C).