It’s not always true, it’s usually at least half true, and in reality it’s practically true.
Truth can be confusing, can’t it? Let me explain …
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Replacing the motherboard is pretty darned close to building a new machine from scratch. It really is the heart and soul of a machine, as well as it’s brain. And with so many so called “peripheral” devices placed directly on the motherboard, you could be changing out a lot more than you might think of.
Now, “it’s not always true” because there are certainly situations where it may not be necessary, but it really requires being on top of exactly what’s being replaced. If you were to replace a motherboard with the exact same kind of motherboard, a reinstall might not be necessary. Similarly, it’s possible that within certain motherboard families you can get away with not re-installing the operating system. Heck, it might even kinda sorta work with some boards that aren’t even related. But I sure wouldn’t want to bet on “kinda sorta” on my PCs.
It’s “usually half true” because technically you don’t have to reformat. Reinstall, yes, but the reformat is optional. You can install on top of the old hard disk’s contents if you like without the reformatting step.
It’s “practically true”, because if you’re going to reinstall anyway, it makes practical sense to clean up the hard drive with a reformat before you do so. Take advantage of the opportunity.
So my advice: I’d always plan on backing up, and then reformatting and reinstalling on a motherboard change, unless it was exactly the same motherboard.