Did Propet (pbuh) really do mut'ah?

I had earlier made a post showing that doing mut'ah is a sunnah of the Prophet (pbuh) himself (click link) as well as a post showing the extreme desirability of mut'ah (click link). But are those ahadith authentic as per the modern ahadith classification system (read more about the modern hadith classification system here: link)?

Shaikh Murtadha al Basha answers the doubters (link).

الشبهة :

هل تزوّج رسول الله – صلى الله عليه و آله – زواج متعة ؟

Doubt: Did the Prophet (pbuh) do mut'ah marriage?.

جواب :

ورد ذلك في الروايات

That is stated in the narrations:

 - وسائل الشيعة - الحر العاملي ج 21 ص 12
 Wasail al Shia- Al Hurr al Amili, Volume 21, Page 12-

( 26388 ) 1 - محمد بن علي بن الحسين بإسناده عن بكر بن محمد ، عن أبي عبد الله ( عليه السلام ) قال : سألته عن المتعة ؟ فقال : إني لأكره للرجل المسلم أن يخرج من الدنيا وقد بقيت عليه خلة من خلال رسول الله ( صلى الله عليه وآله ) لم يقضها .

ورواه الحميري في ( قرب الاسناد ) عن أحمد بن إسحاق ، عن بكر بن محمد ، مثله.

سند الحديث : صحيح

(26388) 1: Muhammad b. Ali b. al Hussain by his isnad (chains of narration) from Bakr b. Muhammad, from abi Abdullah (as), he (narrator) said: "I asked him (as) about the mut'ah)." So [Imam (as)] said: "Indeed for I dislike it for a man that he leaves from the world and there remained upon him a habit from habits of the Prophet (pbuh) unfulfilled."

And narrated it Al Humairi in (Qarb al Isnad) from Ahmad b. Ishaq, from Bakr b. Muhammad, similar to it.

Sanad (chain of narration) of the hadith: Sahih (Correct/Authentic)

( 26389 ) 2 - قال الصدوق : وقال الصادق ( عليه السلام ) : إني لأكره للرجل أن يموت وقد بقيت عليه خلة من خلال رسول الله ( صلى الله عليه وآله ) لم يأتها ، فقلت : فهل تمتع رسول الله ( صلى الله عليه وآله ) ؟ قال : نعم وقرأ هذه الآية : ( وإذ أسر النبي إلى بعض أزواجه حديثاً - إلى قوله : - ثيبات وأبكاراً ) .

سند الحديث معتبر على رأي بعض العلماء .

(26389) - Said al Sadooq: And said al Sadiq (as): "Indeed for I dislike it for a man that he dies and there remained upon him a habit from habits of the Prophet (pbuh) unmet." So I (narrator) said: "So did the Prophet (pbuh) do mut'ah?" [Imam (as)] said: "Yes." And recited this ayah (verse of Qura'n): ""When the Prophet confided a fact unto one of his wives " till " widows and virgins."

Sanad (chain of narration) of the hadith is reliable upon the opinion of some scholars.

و هناك روايات أخرى تركناها اختصاراً
And there are other narrations, we left them for brevity.