need to display first and last day of month based on a date in a cell

I have to create a report that shows data was tracked from the first day of the month to the last day of the month. Currently this is pulled from a data file that tracks the use of a room, however if no one uses the room on the first or last day of the month, then it looks like we tracked only part of the month.
For example, if A1 shows 09/03/17 as the first day the room was used and B1 shows 09/29/17 as the last day the room was used, then I'd like A2 to display the first day of that month 09/01/17 and B2 to display the last day of that month 09/30/17.
Thanks for any help

In A2
=EOMONTH(A1,-1)+1

In B2
=EOMONTH(B1,0)