23. Let the vertices be $(0,0),(4,0),(0,3)$ in the coordinate plane forming triangle $\Gamma$. Consider the following five transformations: counterclockwise rotation by $90^{\circ}, 180^{\circ},$ and $270^{\circ}$, reflection across the $x$-axis, and reflection across the $y$-axis. Among the 125 transformations (which can be the same) applied three times, ( ) transformations will return $\Gamma$ to its original position. For example, first rotating by $180^{\circ}$, then reflecting across the $x$-axis, and finally reflecting across the $y$-axis, $\Gamma$ will return to its original position, but first rotating by $90^{\circ}$ and then reflecting across the $x$-axis twice, $\Gamma$ will not return to its original position.
(A) 12
(B) 15
(C) 17
(D) 20
(E) 25
23. A.

Notice that in any combination of transformations performed, the number of symmetry transformations must be even. This is because each symmetry transformation of triangle $\Gamma$ changes its orientation, and once $\Gamma$ is flipped once, no rotational transformation can restore it to its original position. Only by flipping $\Gamma$ again can it return to its original orientation. Therefore, in the three transformations, the number of symmetry transformations must be even, i.e., either 0 times or 2 times.
We will consider the cases separately.
(1) Rotate 3 times, reflect 0 times.
$\left\{90^{\circ}, 90^{\circ}, 180^{\circ}\right\}: \frac{3!}{2!}=3$,
$\left\{270^{\circ}, 270^{\circ}, 180^{\circ}\right\}: \frac{3!}{2!}=3$.
(2) Rotate 1 time, reflect 2 times.
$\left\{x\right.$-axis, $y$-axis, $\left.180^{\circ}\right\}: 3!=6$.
Thus, the required result is $2 \times \frac{3!}{2!}+3!=6+6=12$.