Formula to Count Unique Customer by Month

Hello,

I am trying to get to a new client count by month. So I have two columns (Customer ID and Customer Start Date) with duplicate records. Thank you so much in advance!

Data Provided
Customer ID (Column A)
1) 23
2) 24
3) 25
4) 24
5) 28
6) 28
7) 30

Month (Column B)
1) 11/1/2009
2) 11/1/2009
3) 12/1/2009
4) 13/1/2009
5) 14/1/2009
6) 12/2/2009
7) 13/2/2009

Answers
- 4 clients in JAN (customer 23, 24, 25 and 28)
- 2 clients in FEB (customer 28 and 30)

Thank you for your help.

Regarding the columns in the original spreadsheet, there are only two.

I expressed myself poorly when I said start date, I was referring to customer purchases in the months.

About the graphic, it's just an expectation of how I wanted it to be. Taking the example you mentioned:
March
In March we had 5 customers, but 1 of them is repeated, so we had 4 customers in March, as a customer bought twice in the same month of March, but on different days.

03/15/2021 25.....> 1st purchase
03/15/2021 22
25/03/2021 25.....> 2nd purchase
03/31/2021 31
03/31/2021 32

Note: I improved the spreadsheet, my question may have been confused.

Hello, Try this:
=SUM(IF(FREQUENCY(IF(($A$6:$A$41>=H$1)*($A$6:$A$41<=EOMONTH(H$1,0)),MATCH($C$6:$C$41,$C$6:$C$41,0)),ROW($C$6:$C$41)-ROW($C$6)+1),1))
Confirmed with CTRL+SHIFT+ENTER
Months in text in the first row replaced with the dates.

Thank you so much, you saved us, we would have to do everything manually one by one.
Again, thank you very much.

You're welcome. Glad to help