Rusian,
This will put the latest date in column A any time you add or change any
information in B

:
Private Sub Worksheet_Change(ByVal Target As Range)
If Not Intersect(Target, Range("B

")) Is Nothing Then
Cells(Target.Row, 1) = Now
End If
End Sub
This will put the date in column A the first time you put information into a
row in B

, but won't change it if you add or change information later in a
row that already has a date in column A.
Private Sub Worksheet_Change(ByVal Target As Range)
If Not Intersect(Target, Range("B

")) Is Nothing And
IsEmpty(Cells(Target.Row, 1)) Then
Cells(Target.Row, 1) = Now
End If
Paste it from here into the sheet module in the VBE.