image - Increase DPI in photoshop -

I'm totally new to Photoshop and I need to do something that I really do not know.

I got a picture with 100 dpi. We want the image to be printed on the poster. I have to increase the 300 dpi to that 100 dpi.

In Photoshop, I went to the image / image size. I unselected "Response image", switched from 100 pixels / inch to 300, but the document size has decreased. The thing is that I do not want to change the poster size. Is "document size" similar to the poster size? If so, what should I do to protect the actual size with the increase of 100 dpi to 300 dpi? Is it a better solution to increase image size than 3x?

Thank you.

Photoshop, for all its strengths, is still a raster image editor in the core. DPI settings are only a conversion factor if you want a larger image, you need to increase the size of the canvas, or reduce the dpi setting

like

  100x100 image @ 100dpi = 1 "x 1" image 100x100 image @ 200 dpi = 0.5 "x 0.5"   
 To increase the size of the printed images, you have to reduce the DPI count Required, so that  
  100x100 image @ 5dpi = 20 "x 20"