Answer: He is not correct. The resulting will be in a different quadrant.
Step-by-step explanation: This would be much easier to answer with a screen shot of the image.
For example, if the original image is in quadrant 1, the first reflection over the x-axis places the new image in quadrant 4, "upside-down" and the second reflection over the y=x line places the new image in quadrant 2 and "oblique" to the original.
Reflecting the original over the y=-x line places the new image in quadrant 3.