1. Let the set $S=\left\{A_{0}, A_{1}, A_{2}, A_{3}\right\}$, and define the operation “ $\oplus$ ” on set $S$: $A_{i} \oplus A_{j}=A_{k}$, where $k$ is the remainder of $i+j$ divided by 4, $i, j \in\{0,1,2,3\}$. Then the number of $x(x \in S)$ that satisfies the relation $(x \oplus x) \oplus A_{2}=A_{0}$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
- 1. B.

From $(x \oplus x) \oplus A_{2}=A_{0}$, let $x \oplus x=A_{k}$, then
$$
\begin{array}{l}
A_{k} \oplus A_{2}=A_{0}, k=2 \\
\Rightarrow x \oplus x=A_{2} \\
\Rightarrow x=A_{1} \text { or } A_{3} .
\end{array}
$$