Will the modified "Fisher–Yates shuffle" implementation remain random?

As we know, Fisher–Yates shuffle give the following "modern algorithm" code:

  To shuffle an array a of n elements (indices 0..n-1):
  for i from 0 to n − 1 do
       j ← random integer with **i** ≤ j < n
       exchange a[j] and a[i]

My question is: if I change i in "i ≤ j < n" to 0, will the algorithm also be random as the algorithm above and how prove? The modified code is:

  To shuffle an array a of n elements (indices 0..n-1):
  for i from 0 to n − 1 do
       j ← random integer with **0** ≤ j < n
       exchange a[j] and a[i]