Yeah, but that reason is nonsense. The Sobel operator uses convolution to approximate the magnitude of the gradient. It doesn't "look for" anything. And since

Yeah, but that reason is nonsense. The Sobel operator uses convolution to approximate the magnitude of the gradient. It doesn't "look for" anything. And since it's the magnitude of the gradient that Sobel finds, Sobel(Invert(img)) is mathematically equivalent to Sobel(img). The invert step is essentially an expensive noop.