Microwave ovens work by causing liquid water pieces (molecules) to vibrate really fast. That vibration causes the water to heat up, which heats up the stuff (food and other water) around it. Eventually the water can vibrate enough that it heats up enough to boil and turn into steam.
Ice cubes are not liquid water, instead they’re made up of water molecules held really tightly together as a solid, technically a crystal. The way that the ice is formed makes it very difficult for the microwaves to vibrate the individual water molecules, so they don’t get moving fast enough to heat up much, so they don’t melt the overall ice cube.
Microwaves heat water inside your food very unevenly. One reason why ice cubes didn’t melt is because they probably absorbed less energy than rice.
Another reason hides in the specific heat capacity of water and the heat of fusion of ice. You need 418,4 Joules of heat to warm up 1g of liquid water from 0°C to 100°C. Meanwhile, it would take 333,55 Joules of heat to melt 1g of ice ( the transition from 0°C solid water to 0°C liquid water). Melting ice and then heating the resulting liquid water takes significantly more energy than just heating liquid water.
So, if you have 1g of 0°C water and 1g of 0°C ice in a microwave and they theoretically absorb an equal amount of energy, water will be already hot while ice will only slightly melt (but still stay at 0°C).
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