With some help from my little friend Sargum, I started with a 288X288 pixel file, converted it to a low quality JPEG, and rotated it four times (saving each time), to get back to the original orientation. This is a large amount of abuse! Normally, we would not subject photos to such things. However, Photoshop does pretty well. The initial JPEG has little error, and the error only increases by a small amount during the four rotations. Any additional error is not objectionable. However, the error does increase some; a rotation is not totally lossless! More about this later...