Answer
The plane mirror is actually not reversing left and right, it is just showing you the object that is opposite to it. And to discuss whether it reverses up and down, or not, we need a horizontal mirror suspended above our heads to compare, as the author mentioned in the problem. You can also see that you see your head first and then your feet as if your image is upside down, but that is not true. The mirror is not reversing you it showing objects from the closest to the farthest and in the mirror above your head, your head is the closest to the mirror and your feet now is farthest, so you see that it as if it is upside down.
But yes, the mirror reverses front and back. If you are standing in front of a vertical mirror, you can't see your back, you see your face.
That's because it reverses front and back.
Work Step by Step
The plane mirror is actually not reversing left and right, it is just showing you the object that is opposite to it. And to discuss whether it reverses up and down, or not, we need a horizontal mirror suspended above our heads to compare, as the author mentioned in the problem. You can also see that you see your head first and then your feet as if your image is upside down, but that is not true. The mirror is not reversing you it showing objects from the closest to the farthest and in the mirror above your head, your head is the closest to the mirror and your feet now is farthest, so you see that it as if it is upside down.
But yes, the mirror reverses front and back. If you are standing in front of a vertical mirror, you can't see your back, you see your face.
That's because it reverses front and back. And if you need an image that takes the same position as you, like two men in one row, you can't use one mirror because the mirror only shows what is in front of it. So then, you need two mirrors, one in front of you and one behind you, to repeat the reflections and then you can see your back.
From all the above, the mirror does not reverse right and left or up and down.