In plain words
Because it is beginningless and free from guṇas, this imperishable Paramātma, though dwelling in the body, neither acts nor is tainted, son of Kunti.
Word for word
Because beginningless, because without guṇas, this supreme Self, imperishable, though abiding in the body, O son of Kuntī, does not act [and] is not tainted.
अनादित्वान्निर्गुणत्वात् परमात्माऽयमव्ययःशरीरस्थोऽपि कौन्तेय न करोति न लिप्यते
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
एकस्य आत्मानः सर्वदेहात्मत्वे तद्दोषसम्बन्धे प्राप्ते, इदम् उच्यते —
अनादित्वात् अनादेः भावः अनादित्वम् , आदिः कारणम् , तत् यस्य नास्ति तत् आनादि । यद्धि आदिमत् तत् स्वेन आत्मना व्येति ; अयं तु अनादित्वात् निरवयव इति कृत्वा न व्येति । तथा निर्गुणत्वात् । सगुणो हि गुणव्ययात् व्येति ; अयं तु निर्गुणत्वाच्च न व्येति ; इति परमात्मा अयम् अव्ययः ; न अस्य व्ययो विद्यते इति अव्ययः । यत एवमतः शरीरस्थोऽपि, शरीरेषु आत्मनः उपलब्धिः भवतीति शरीरस्थः उच्यते ; तथापि न करोति । तदकरणादेव तत्फलेन न लिप्यते । यो हि कर्ता, सः कर्मफलेन लिप्यते । अयं तु अकर्ता, अतः न फलेन लिप्यते इत्यर्थः ॥
कः पुनः देहेषु करोति लिप्यते च ? यदि तावत् अन्यः परमात्मनो देही करोति लिप्यते च, ततः इदम् अनुपपन्नम् उक्तं क्षेत्रज्ञेश्वरैकत्वम् ‘क्षेत्रज्ञं चापि मां विद्धि’(भ. गी. १३ । २) इत्यादि । अथ नास्ति ईश्वरादन्यो देही, कः करोति लिप्यते च ? इति वाच्यम् ; परो वा नास्ति इति सर्वथा दुर्विज्ञेयं दुर्वाच्यं च इति भगवत्प्रोक्तम् औपनिषदं दर्शनं परित्यक्तं वैशेषिकैः साङ्ख्यार्हतबौद्धैश्च । तत्र अयं परिहारो भगवता स्वेनैव उक्तः ‘स्वभावस्तु प्रवर्तते’(भ. गी. ५ । १४) इति । अविद्यामात्रस्वभावो हि करोति लिप्यते इति व्यवहारो भवति, न तु परमार्थत एकस्मिन् परमात्मनि तत् अस्ति । अतः एतस्मिन् परमार्थसाङ्ख्यदर्शने स्थितानां ज्ञाननिष्ठानां परमहंसपरिव्राजकानां तिरस्कृताविद्याव्यवहाराणां कर्माधिकारो नास्ति इति तत्र तत्र दर्शितं भगवता ॥ ३१ ॥
In plain words
If one single Self is really the Self of every body, then it might seem to follow that this Self picks up all the flaws of every one of those bodies too. Here's the answer to that worry.
Let's unpack 'beginningless'. A beginning simply means a cause; whatever has no cause behind it is beginningless. Now, anything that had a beginning is, by its very nature, bound to end — that's just how things with a starting point work. But this Self has no beginning and no parts, so it simply doesn't end. The same holds for another reason too: anything with qualities ends when those qualities wear off, but this Self has no qualities at all, so there's nothing there to wear off either. That's exactly why the Supreme Self is called imperishable — there's simply no decay to be found in it, ever. Given all that, why is it still called 'situated in the body'? Only because it's within a body that the Self ever gets noticed or perceived — that's the whole reason for the phrase, nothing more. And even so, it never actually does anything. And precisely because it never acts, it's never touched by the results of action. Whoever actually acts gets stained by what that action produces. But this Self isn't an agent at all — so nothing it 'does' ever sticks to it.
So who actually acts, and who actually gets tainted by that action, right here in the body? If we say the embodied self is simply different from the Supreme Self, and that this different self is the one doing the acting and picking up the taint, then everything already taught about their oneness — 'know Me also as the field-knower' — falls apart. But if we say there's no embodied self apart from the Lord at all, then the question just comes right back: who acts, who gets tainted? That question can't be waved away. And it certainly can't be dodged by saying the Supreme simply doesn't exist because it's too unknowable and unspeakable to talk about — which is exactly the move that led the Vaiśeṣikas, the Sāṅkhyas, the Jains, and the Buddhists to abandon this Upaniṣadic teaching altogether. Here's the resolution, and it comes straight from the Lord's own words: 'it is nature that acts.' Acting and being tainted are simply how things get described at the level of ignorance — that's all those words really are, a manner of speaking that belongs to that level. In ultimate truth, none of it touches the one Supreme Self at all. And that's exactly why someone who has settled into this deepest discernment, who lives entirely for knowledge, the paramahaṃsa renunciate who has set aside every ignorance-based way of speaking and acting — such a person simply has no further business with ritual action. The Lord shows this again and again, throughout this whole teaching.
Close to the Sanskrit
Given that, the one Self being the Self of all bodies, a connection with their defects would follow, this is now stated —
Because of beginninglessness: the state of the beginningless is beginninglessness; a beginning means a cause; that which has none of that is 'beginningless'. For whatever has a beginning passes away by its own nature; but this Self, because of beginninglessness, being partless, does not pass away. Likewise, because of being without qualities: for that which has qualities passes away through the passing away of its qualities; but this Self, because of being without qualities, does not pass away either; thus this Supreme Self is imperishable — no passing away of it exists, hence 'imperishable'. Since this is so, therefore, though called 'situated in the body' — because the apprehension of the Self occurs only within bodies is it called 'situated in the body' — even so it does not act. Precisely because of this non-acting, it is not tainted by that action's fruit. For whoever is an agent is tainted by the fruit of action; but this Self is no agent, therefore it is not tainted by fruit: that is the meaning.
But who, then, acts and is tainted within bodies? If, to begin with, the embodied self is different from the Supreme Self, and acts and is tainted, then this teaching already given — the oneness of kṣetrajña and Īśvara, 'know Me also as the field-knower' (Bhagavad Gītā 13.2), and so forth — becomes untenable. Or, if there is no embodied self other than the Lord, who then acts and is tainted? This must be answered; or, one might say the Supreme does not exist, on the ground that it is in every way unknowable and inexpressible — and thus the Upaniṣadic doctrine declared by the Lord has been abandoned by the Vaiśeṣikas, Sāṅkhyas, Jains, and Buddhists. In this regard, this very resolution has been stated by the Lord himself: 'it is nature that operates' (Bhagavad Gītā 5.14). For it is only a usage whose nature is mere ignorance that gives rise to the expressions 'acts' and 'is tainted'; but in ultimate reality, that does not exist in the one Supreme Self. Therefore, for those established in this ultimate discernment of Sāṅkhya, devoted to knowledge, the paramahaṃsa wandering renunciates, for whom every ignorance-based usage has been set aside, there is no entitlement to ritual action — this has been shown repeatedly by the Lord throughout the text.