Depends on the car. If you tried that with an old 4WD VW Vanagon, you would blow the transmission, but most cars are not that sensitive.
As @Tropical_Willie points out, new tires are not the same size as used tires. The difference in size puts a little wear on the differential in the transaxle. It also messes up the operation of ABS and other electronic driving aids. Some cars can handle that, some cannot. Those with 4WD/AWD will often wind up with damaged transfer cases and/or transmissions.
That said, I ran my old (‘87) Corolla with severely mismatched fronts (a 175/70 and a 185/65), but only because I knew for a fact that that thing was built like a brick shithouse. If that Corolla is an ‘88 or newer, it isn’t built nearly as ruggedly though. Simple test; drive at 35 mph and shift it into reverse; if the transmission survives, then it’s tough enough to handle mismatched tires. (That’s how I found out how tough my Toyota was; I accidentally did that!) If the transmission fails, or you just don’t have the courage to try, then buy in pairs.
@SecondHandStoke When I got a new pair, they insisted on having the worn tires on the front. Apparently it’s the law now.