how to save illustrator file in PDF with keeping the original artbord size

[settsun]

I created an illustrator file with the size of 1200 x 1200 pixels, RGB color, 300dpi.

I want to save this file with PDF without changing the file size of 1200 x 1200 pixels and 300dpi.

However, when I choose PDF and do nothing, then the file size become bigger with 3258 x 4624 pixels.

How do I keep the original size with 300 dpi and still save as PDF?

[Doug A Roberts]

Are you sure we are talking about PDF here? Where in the PDF options do you set the file to 300 PPI?

[Monika Gause]

What exactly are you doing step by step and exactly how do you check document size?