Problem with counting item in adjacent cell if the cell in a particular column is empty

Good day everyone!

I am currently faced with the problem of not being able to count items in an adjacent cell if the cell in a particular column is empty.

I have submitted a sample file for anyone to take a look.

So basically, the main column I want to count is column B. So for example, I want to count the number of "A" in column B, and if a cell in column B is empty, say if cell B5 is empty, I'd go to cell A5 to see if the data in that cell is "A", and if it is, I'd add it to my tally.

I have tried using

=COUNTIFS($B:$B,"A",$B:$B,=IF($B:$B="",=countif($A:$A,"A")))

to do the job but it doesn't seem to work and I have no idea why!

It'd be great if anyone could help me out on this!