1. Given the sets
$$
A=\{1, b, a+b\}, B=\{a-b, a b\} \text {, }
$$

and $A \cap B=\{-1,0\}$.
Then the values of $a$ and $b$ are ( ).
(A) $-1,0$
(B) $0,-1$
(C) $-1,1$
(D) $1,-1$
-,1. A.
From $1 \notin A \cap B$, we know that one of $b$ or $a+b$ must be 0, and the other must be -1.

Since $a \neq 0$ (otherwise, the elements in set $A$ would contradict the principle of distinctness), therefore, $a=-1, b=0$.