What is Reddit's opinion of BLACK+DECKER Jig Saw, 4.5 -Amp (BDEJS300C)?
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3 reviews of this product found across Reddit:

Yes, but it will take forever (comparatively) and you'll likely end up going through multiple blades. Just get a cheap jig saw (or get the DeWalt 20v max if you want a good long-lasting one that matches you collection. It is excellent!). You don't need anything fancy or high-powered for this job. This $30 B&D would be more than sufficient.

If the back of the shelf is just cheap particle board, you should just cut a hole in it. I am not someone who's handy with tools, but all i did was pick up a $25 Jigsaw, used screwdriver to just twist and punch a hole where I wanted to start, and then just stuck the jigsaw in and cut a large square hole behind my stuff. $1 piece of sandpaper later to get rid of all the jagged edges, and boom, I had a really well ventilated media center.

How to cut stall mats: https://www.amazon.com/BLACK-DECKER-Jig-Amp-BDEJS300C/dp/B00OJ72L84/ Edit: A chalk line makes for great marking of cut lines. Also, the saw obviously requires cutting the mat while it overhangs a thick board, plank of wood, workbench... or something similar.