Was Alexander Hamilton a classmate of Jonathan Dayton and Brockholst Livingston at Elizabethtown Academy?

A short excerpt fromAlexander Hamilton: The Formative Years, including the relevant endnotes:

According to John C. Hamilton, Alexander Hamilton at Elizabethtown Academy studied alongside Jonathan Dayton, afterwards speaker of the House of Representatives; Brockholst Livingston, subsequently a judge of the Supreme Court of the United States, and others who became of note.* However, Henry Brockholst Livingston, or Brockholst Livingston as he was known to differentiate him from his cousin Henry...