2. Let the fractional equation about $x$ be $\frac{a-2}{2-x}=\frac{a-2}{x-2}$ with infinitely many solutions. Then the number of values for $a$ is ( ).
(A) 0
(B) 1
(C) 2
(D) Infinitely many
2. B.

Since the fractional equation has a solution, we have
$$
a-2=2-a \Rightarrow a=2 \text {. }
$$

Therefore, $a$ has only 1 value.