The Inca Empire was called Tawantinsuyo in Quechua, which means "four regions". The empire only lasted for about 100 years as the arrival of the conquering Spaniards in 1532 marked the end of their reign. Their main language was Quechua, but as the Incas were basically made up of many different groups there were probably many different languages as well.
The Inca Empire began around Lake Titicaca in about 1197. From 1438 to 1533, the Incas used conquest and non-violent assimilation to gain a large portion of western South America, that centered on the Andean mountain ranges. It included large parts of what is now Ecuador, Peru, Bolivia, Argentina and Chile.
( from Wikipedia )