Why did Allaah invite Prophet Muhammad, sallallaahu ʻalayhi wa sallam, to see the heaven(s) and hell, and not any other prophet before him?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.

If you mean the ascension of the Prophet, sallallaahu ʻalayhi wa sallam, to the heavens with his body and soul on the night of Israa' (Night Journey) and Miʻraaj (Ascension to Heaven), then you should know that this was authentically established. It was a special honor bestowed by Allaah particularly on His Messenger, sallallaahu ʻalayhi wa sallam. Ibn ʻUthaymeen wrote:

“The ascension of the Prophet, sallallaahu ʻalayhi wa sallam, to the heaven was one of the special honors conferred particularly on him, and none of the past Prophets of Allaah was granted such an honor, and it will not be bestowed upon anyone else after him, except the soul of the believer. Once extracted from the body, the angels wrap the believer's soul in a shroud that smells of musk and ascend up to the heavens. As for the angels, it is a totally different story. The honor of the ascension to heaven was peculiar to the Prophet, sallallaahu ʻalayhi wa sallam, and was not conferred on any of the past Prophets; Allaah has honored him, sallallaahu ʻalayhi wa sallam, with perfect honor over all those who were before him.

He, sallallaahu ʻalayhi wa sallam, ascended up to the seventh heaven until he reached the place where the sound of the scratching of Pens, which record the Divine Decree, could be heard. He, sallallaahu ʻalayhi wa sallam, reached Sidrat Al-Muntaha (i.e. lote-tree of the utmost boundary, beyond which none can pass), the farthest anyone ascending from the earth to the heaven could reach; we know of no other human being to have reached such a place other than the Prophet, sallallaahu ʻalayhi wa sallam.

This was a special honor bestowed on the Prophet, sallallaahu ʻalayhi wa sallam, in particular, and it was not granted to any other Prophet of Allaah. It is one of the great signs indicating the perfect and infinite power of Allaah, and it emphasizes the great signs shown to the Prophet, sallallaahu ʻalayhi wa sallam, during this journey...” [Excerpted with slight modifications]

Among the reported scenes shown to the Prophet, sallallaahu ʻalayhi wa sallam, during his ascension to heaven are those of Paradise and Hellfire. Huthayfah ibn Al-Yamaan said, “The Messenger of Allaah, sallallaahu ʻalayhi wa sallam, was brought a riding beast with a long back - stretching out like this - one stride of it is as far as his vision. So, the two of them (the Prophet and the angel Jibreel [Gabriel]) remained upon the back of Al-Buraaq until they saw Paradise and Hellfire and all which has been prepared for the Hereafter, then they returned back to where they began.” [At-Tirmithi graded it hasan saheeh (good or sound)]

Moreover, the hadeeth reported about the incident of Al-Israa' wa Al-Miʻraaj reads, “... until he (Jibreel) took me to Sidrat Al-Muntaha, which was shrouded in colors, indescribable. Then I was admitted into Paradise, where I found small tents (made) of pearls, and its earth was of musk.” [Al-Bukhari and Muslim]

Distinguishing the Prophet, sallallaahu ʻalayhi wa sallam, with the special honor of the ascension to heaven aside from all the other Prophets of Allaah, may Allaah exalt their mention, is one of the special honors bestowed upon him and was not granted to anyone else so as to indicate his refined status and elevated rank; he, sallallaahu ʻalayhi wa sallam, is the best of mankind.

Allaah knows best.