In the Hadith of Thaqalayn
Hadith of Thaqalayn implies the knowledge authority of the Ahl al-Bayt (a), because the Prophet (s) asked Muslims to adhere to the Qur'an and his Ahl al-Bayt (a) so that they do not go astray.
The first and most essential knowledge reference and authority of Muslims is the glorious Qur'an and after that the tradition of the Prophet (s). Regarding this, the role of the Ahl al-Bayt (a) is that they are interpreters of the Qur'an, guardians and transmitters of the tradition of the Prophet (s). Surly, the Prophet (s) explained a great part of the facts and teachings of the Qur'an for people, but he (s) left another part the conditions for explaining which were not provided or it was more appropriate for them to be explained later to his infallible Ahl al-Bayt (a) to explain. Thus, full guardianship of what the Prophet (s) had explained and what was not explained yet was given to the Ahl al-Bayt (a).
The true way of knowing the Qur'an and the tradition of the Prophet (s) is adhering to the Ahl al-Bayt (a) of the Prophet (s), thus they are the knowledge authority of Muslims for knowing religious teachings and rulings.
The Sunni scholar Mulla 'Ali Qari, "Ahl al-Bayt [people of the house] are usually more knowledgeable about the owner of the house and his state; therefore, the Ahl al-Bayt (a) are the most knowledgeable ones to the conduct of the Prophet (s), his manner, his rules and wisdom and that is why they deserve to stand beside the Book of God, the Almighty."
Also, Ibn Hajar said, "The Prophet (s) called the Qur'an and 'Itra [Ahl al-Bayt (a)] as Thiql [weight]; since, a valuable and important thing is called Thiql and the Qur'an and the Ahl al-Bayt (a), because both of them are mines of divine knowledge, great secrets and wisdom and religious rulings; therefore, adherence to them and learning knowledge from them has been encouraged and emphasized. This emphasis about the Ahl al-Bayt (a) is about those who know the Book of God and the conduct of the Prophet (s) and they are those who will never separate from the Qur'an until the Day of Judgment.
In the Verse of Tathir
In the verse of Tathir (33:33), the glorious Qur'an introduces the Ahl al-Bayt (a) as those whom God has desired to repel all impurity from and also has mentioned that sublime facts and teachings hidden in the Qur'an cannot be found expect by those purified from all impurity. Just the same way that the physical purity is required for touching the text of the Qur'an, purity of the soul from vices is required for understanding the teachings of the Qur'an and the more delicate and deeper the teachings of the Qur'an are, the higher purity of souls are needed to understand them and the greatest of them require infallibility. Therefore, teachings of the Qur'an are not fully and deeply known by anyone other than the Prophet (s) and the Infallible ones (a) and thus to learn them, one needs to refer to them.
Imam al-Sadiq (a) said, "The facts about the past and future and rulings which distinguish the truth and falsehood about the life of human being are mentioned in the Qur'an and we know them." There are many hadiths narrated from Imams (a) in this regard.