Gabriel’s problem

Gabriel wrote the numbers 1-9 in a 3×3 grid.

He then multiplied together all the numbers in each row and wrote the resulting product next to that row.
He also multiplied the numbers in each
column together, and wrote the product
under that column.
He then rubbed out the numbers 1-9.

Can you work out where Gabriel placed the numbers 1-9?

Did you have more information than you needed?

This puzzle comes directly from this NRich page, with the pdf of the problem available here.