Al-jawab billahi at-taufeeq (the answer with Allah’s guidance)
No, this is not true.
It is not permissible to fast during the three days (11th,12th and 13th) following the ‘Id Adha. Abu Hurairah reported that the Messenger of Allah, Sallallahu Alaihi Wasallam, sent ‘Abdullah ibn Huzhaqah to announce at Mina: “You are not to fast these days. They are days of eating and drinking and remembering Allah.” This is related by Ahmad with a good chain.
Ibn ‘Abbas reported that the Messenger of Allah, Sallallahu Alaihi Wasallam, sent a person to announce: “Do not fast on these days, as they are days of eating, drinking and rejoicing with one’s family.” At-Tabarani related it in al-‘Awsat.
The fast of ‘Youmul Arafah’ (9th) has been emphasised by the Prorhet (Sallallahu Alaihi Wasallam) as a Mustahab act. According to a Hadith, the fast of this day becomes a cause, hopefully so, of forgiveness for sins committed in one year. (Islamic Months, Pg. 12, by ‘Mufti Taqi Uthmani’)
It is reported that Prophet (Sallallahu Alaihi Wasallam) used to fast the (first) nine days of Zul Hijjah.
Hafsah (Radhiallahu Anha) reports that Rasulullah (Sallallahu alayhi wasallam) used to fast the (first) nine days of Zul Hijjah. (Nasa’ee, Ahmad, Aboo Dawood)
And Only Allah Ta’ala Knows Best.
Moulana Qamruz Zaman