ऋतो ङिसर्वनामस्थानयोः

Operational rule vidhi

The last letter of a ऋदन्त word is replaced by अर् in presence of - (a) ङि-प्रत्यय and (b) a प्रत्यय that is also a सर्वनामस्थान.

Word by word (padaccheda)

Target ऋतः ṣaṣṭhī · ekavacanaRight context ङिसर्वनामस्थानयोः saptamī · dvivacana

Target Ṣaṣṭhī (6th case): names what gets replaced, "in place of X" (1.1.49 षष्ठी स्थानेयोगा).
Right context Saptamī (7th case): "when X follows", the operation applies to what precedes (1.1.66 तस्मिन्निति निर्दिष्टे पूर्वस्य). Also a condition or domain ("in the sense of").

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Full reading

ऋतः ङिसर्वनामस्थानयोः

Pāṇini leaves out words that carry over from earlier sūtras. Expand to see the rule as a reader actually understands it.

Commentary

गुण is substituted for the final ऋ of a अङ्ग (stem) in the Locative -7th case singular and in the strong cases.
As मातरि, पितरि, भ्रातरि, कर्तरि; मातरौ, पितरौ, भ्रातरौ, कर्तारौ, कर्तारः ॥ For the long in कर्तारौ and कर्तारः see 6.4.11. The त् in ऋत् is for the sake of facility of utterance.

Because before ङि and strong cases, it is impossible for a stem to end in a long vowel ॠ nor a dhatu noun can so come, since in that case, long ॠ would be changed to इर् by 7.1.100, and in forms like कर्तॄणि there is नुम् ॥

Śrīśa Chandra Vasu, The Ashtadhyayi of Panini (1897), via ashtadhyayi.com.