Rotate about a point or an axis?

Question

1. English is not my native language. Why math text uses the preposition "about" while referring rotation in the context of a point, an axis or a plane? Is not the preposition "around" or "on" more natural to use in this context?
2. Is matrix multiplication of NON-square matrix and identity matrix commutative?
3. Scale applies along an axis. For example, if you scale along x-axis, the horizontal length of the shape will increase/decrease in 2D. Why the author of the following para (whole para is pasted below to clear the context) is saying that it is applied about the perpendicular axis? Also, why did he use the preposition "about" here?

Scaling along the Cardinal Axes The simplest scale operation applies a separate scale factor along each cardinal axis. The scale along an axis is applied about the perpendicular axis (in 2D) or plane (in 3D). If the scale factors for all axes are equal, then the scale is uniform; otherwise, it is nonuniform.

Please help if you can answer any one of the three questions.

Thanks.

Answer 1

"around" is pretty common too; this is more a question for the English language stacks, but I know that "about" was more commonly used in the past the way "around" is now; see for instance this passage from Shakespeare's Macbeth.

O well done! I commend your pains;

And every one shall share i' the gains;

And now about the cauldron sing,

Live elves and fairies in a ring,

Enchanting all that you put in.

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A matrix that isn't square can only be multiplied on both sides by another matrix that isn't square: a $2\times3$ matrix can only be multiplied on both sides by a $3\times2$ matrix. The results of these two multiplications are both square matrices, of different sizes: if $A$ is $2\times3$ and $B$ is $3\times2$, then $C = AB$ is a $2\times2$ matrix, and $D = BA$ is a $3\times3$ matrix. Because they are different sizes, $C$ and $D$ are obviously not equal; because they are not square, neither $A$ nor $B$ can be an identity matrix.

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The final passage is ... not how I would put things, but I think what he means is - a scaling along a particular axis fixes its perpendicular: in 2 dimensions, a scaling along one axis leaves a line perpendicular to the axis unchanged, and in 3 dimensions it similarly leaves a plane perpendicular to the axis unchanged. This sense of "about" is shared with rotation, in that in both cases these operations leave the things they are "about" unchanged.