Why don't you mention that Chalukyas were allied with Gurjara Pratiharas (Gujarat) and Mewar (Rajasthan) in those wars with Arabs. These kingdoms weren't bickering about North vs South then as some are in this thread.Colonial European powers never had the manpower to change the culture or language of the native people.
But invaders like the Aryans, Arabs and Turks did have the manpower to change the culture and language of
the native people. Fortunately southern India was protected by the Chola, Chera and Pandya Kingdoms
against the Aryans during ancient period and during the medieval period southern India was protected
by the Chalukya Dynasty and Vijayanagar Empire against the Arabs and Turks. This is the main reason
why many north Indians and Persians are Muslims and even use the Arab alphabet as they were conquered
by the Arabs and Turks.
https://en.wikipedia.org/wiki/Battle_of_Rajasthan
Also, Cholas claimed descent from a Shibi Raja who's story appears in Mahabharat and Jatakas. This king was from western Punjab, Pakistan.
https://en.wikipedia.org/wiki/Sibi_Jataka#Connections_with_the_Chola_Dynasty
https://archive.org/stream/TribesInAncientIndia#page/n99/mode/2up
It is said that Solankis in Guj/Rajesthan/MP and Rathods also came from South Indian dynasties like Chalukyas and Rashtrakutas.
Heard of Chandragupta Maurya ? Born in Magadha (Northern India), died in Karnataka's Bhadrabahu caves as a Jain ascetic(Southern India). His Guru (Chanakya) from Kerala (Southern India), went onto study in Takshishila (Pakistan), chose to live in Magadha (Northern India). 2000 years ago. India has always been 1 civilization. So don't get so uptight over half baked North-South construct created by British that is less than 150 years old.