Question 139
Two transformations are said to *commute* if applying the first followed by the second gives the same result as applying the second followed by the first. Consider these four transformations of the coordinate plane:
* a translation 2 units to the right,
* a $90^\circ$-rotation counterclockwise about the origin,
* a reflection across the $x$-axis, and
* a dilation centered at the origin with scale factor $2$.
Of the $6$ pairs of distinct transformations from this list, how many commute?
(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$
* a translation 2 units to the right,
* a $90^\circ$-rotation counterclockwise about the origin,
* a reflection across the $x$-axis, and
* a dilation centered at the origin with scale factor $2$.
Of the $6$ pairs of distinct transformations from this list, how many commute?
(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$