How to export png the same size as artboard and keep the same quality

You won't keep the same quality. PNG is a pixel image. You cannot zoom in.

That depends on your ultimate objectives for the graphic. I almost never work in Illustrator when the output is to be a raster image, but on those rare occasions when I have, I was never satisfied with raster-format export. If the PNG-destined elements are simple, set up a Photoshop canvas at the desired final size and resolution, then simply copy and paste from Illustrator. For more complex artwork, save (in Illustrator) as PDF, then open that in Photoshop to rasterize at the desired final size/resolution. In either case, PNG output from Photoshop will offer more control and better results.

This may sound unforgivably outdated and boring, sorry.

If you wish to have PNGs (PNG24, of course) look crisp and clean, it is important to have the images in the exact desired final pixel x pixel size, forget about resolution which may actually lead to wrong sizes and hence blurriness. It is easiest and safest to work at the desired size.

A very common unsuitable way is to Export to PNG (remember to use PNG24 and use Transparency for artwork to be in front of different backgrounds) with a medium or high resolution, such as 300PPI.

To retain the clean and crisp artwork, a PNG must be created at exactly the pixel x pixel size that it is to be used for (or second best at sizes that are powers of 2 times as large).

For clean and crisp artwork avoid JPEG.

It is also important to have the artwork and also the Artboard placed fully within integer/whole pixel X and Y values in the Workspace. Otherwise the resulting image will become a bit wider/taller and the extension(s) will be empty and therefore be white.

Therefore, the safest way is to create the artwork at the final pixel x pixel size and use a corresponding Artboard, then either use the Legacity Save for Web (where you can look in the Image Size window for size confirmation) or Export at 72PPI. In either case, use the relevant optimization (available with both ways); it is also convenient to have 72PPI in the Effect>Document Raster Effect Settings.

If you have pure vector artwork, you can relax a bit and have the artwork/Artboard at any size (the Artboard must have the same proportions as the final image), then use the Legacity Save for Web and set either Width or Height in the Image Size and Apply (make sure the other value is also correct).

The Legacy Save for Web may be an old carthorse, but it knows its way home, even if the driver is drunk and sleeping it off in the hay in the back.