The Canon EOS 5D Mark III has a resolution of 5760 x 3840 pixels, or 22.1 MP. It has a 3:2 (1.5:1) aspect ratio.

A2 sized paper is 16.5 x 23.4 inches (420 x 594 mm). It has a 1.414:1 aspect ratio.

This means we must either:

• Leave blank spaces at the top and bottom of the paper to use the full image width on the width of the A2 paper. This would leave us with 246 pixels per inch (9.69 pixels per mm) covering an area 23.4 inches wide and 15.6 inches high.
• Crop a bit off the ends of the 3:2 image from our camera to use the full height of the paper. This would leave us with 232.73 ppi (9.14 p/mm) covering the full size of the paper, but about 315 pixels would be cropped off the long dimension of the image from the camera.
• "Stretch" our image to fit the height of the paper without losing any of the long ends of the image on the left and right. This would distort the image and make vertical objects look thinner and horizontal objects look fatter. We would have 246 ppi (9.69 p/mm) horizontally and 232.73 ppi (9.14 p/mm) vertically.

Conventional wisdom says we should print at 300 ppi (11.81 p/mm) for a print intended to be viewed at a distance of 10-12 inches.¹ That leaves us just a tad bit short in terms of resolution, as we only have enough pixels for around 233-246 ppi using a 5760 x 3840 pixel image on A2 paper. But a 23.4 x 16.5 inch image is probably going to be viewed from a distance greater than the "standard" 10-12 inches. In the case of an A2 print, we can probably assume a viewing distance of at least twice that. This reduces the angular size of the same pixel pitch as it is viewed by the observer. At twice the viewing distance of 20-24 inches, roughly 150 ppi is enough to give the same pixel pitch in terms of the angle of view to the observer as 300 ppi viewed from 10-12 inches.

For most uses, an A2 print of a full image from a Canon EOS 5D Mark III would be acceptable.

My question is, will an A2 size print be clear enough from a canon 5d iii image (No Crop).

Assuming the image is properly focused and reasonable sharp, it should be clear enough for most conditions under which an A2 size print is viewed.

¹ "Standard" display conditions are an 8x10 inch image size viewed from a distance of 10-12 inches by a person with 20/20 vision.