If we reduce A to reduced echelon form, the leading entries are in the pivot positions of A.

It turns out that we can locate the pivot positions by reducing A to echelon form only.  The entries in these positions are called pivots, while the columns they appear in are called pivot columns.

For example, the matrix

is row equivalent to

and so we know that the pivot positions are those containing red numbers.  Also, the first, second and fifth columns are pivot columns.