Soaking a matte-painted wall with water typically results in the paint lifting. Scrubbing it with an abrasive chemical or scrub brush easily causes the paint to break down and peel. Most high-traffic areas have semi-gloss or eggshell paint with an oil layer that allows for better cleaning. Cleaning matte painted walls requires a light hand, little moisture and working quickly.
Prepare a cleaning mixture that won't break down the paint easily. Simple homemade mixtures like one part vinegar and two parts vinegar are mild and nontoxic. A drop of mild dish soap in water may work, though too much dish soap can break down the paint. If you're out of vinegar, mix 1/4 cup of baking soda in about one cup of water. The baking soda is abrasive, so use the mixture sparingly, for spot cleaning only.
Cover the area below the walls with drop cloths, and move all furniture and fabric away so it doesn't get wet. You're not dealing with harsh chemicals, but it allows for easier cleanup. Move electric cords away as well. Dry clean the wall first by vacuuming or dusting it with a clean rag or feather duster. Take a damp, but not wet, rag with your cleaning solution, and lightly wipe down the dirty area. Pressing and blotting sometimes works as well. Wipe the area with a clean, damp rag, and immediately dry it with a clean, dry rag. Do this with the entire wall.
If your matte-painted walls are considerably dirty, repainting may be the better option. Cleaning too harshly can leave uneven spots, and homes benefit from a fresh coat of paint every few years. Consider semi-gloss or eggshell paints with easy clean formulas so you can use more pressure and a bit stronger cleaning solution when removing dirt from the walls. Cleanable wallpaper can bring color and texture into the room as well.