The statement “An ideal transformer has infinite values of primary and secondary inductances” is false.
An ideal transformer is a theoretical device that has no losses. In reality, all transformers have some losses, which are due to the resistance of the windings, the core losses, and the leakage inductance.
The resistance of the windings causes a voltage drop, which reduces the output voltage. The core losses are due to the eddy currents and hysteresis losses in the core. The leakage inductance is the inductance between the primary and secondary windings, and it causes a current to flow in the secondary winding even when there is no load connected to it.
All of these losses reduce the efficiency of the transformer. The efficiency of a transformer is the ratio of the output power to the input power. A transformer with 100% efficiency would have no losses, and its primary and secondary inductances would be infinite.
However, no transformer can have 100% efficiency, so its primary and secondary inductances are always finite.