6. Let $S=\left\{\left(s_{1}, s_{2}, \cdots, s_{6}\right) \mid s_{i} \in\{0,1\}\right\}$, for any $x, y \in S, x=\left(x_{1}, x_{2}, \cdots, x_{6}\right), y=$ $\left(y_{1}, y_{2}, \cdots, y_{6}\right)$ define:
(1) $x=y \Leftrightarrow \sum_{i=1}^{6}\left(x_{i}-y_{i}\right)^{2}=0$;
(2) $x y=x_{1} y_{1}+x_{2} y_{2}+\cdots+x_{6} y_{6}$.
If a non-empty set $T \subseteq S$, and for any $u, v \in T, u \neq v$, we have $u v \neq 0$, then the maximum number of elements in the set $T$ is ( ).
(A) 62
(B) 52
(C) 42
(D) 32
6. D.

For any $x \in S$, define
$$
x^{-1}=\left(1-x_{1}, 1-x_{2}, \cdots, 1-x_{6}\right) \text {. }
$$

Thus, for any $x \in S$, there exists a unique
$$
x^{-1} \in S \text {, and }\left(x^{-1}\right)^{-1}=x, x \neq x^{-1}, x x^{-1}=0 \text {. }
$$

If $x \in T$, then $x^{-1} \notin T$.
Therefore, the number of elements in set $T$ is at most 32.
Clearly, $T=\left\{\left(x_{1}, x_{2}, \cdots, x_{6}\right) \in S \mid x_{1}=1\right\}$ satisfies the condition. In this case, the number of elements is 32.
In summary, the maximum number of elements in set $T$ is 32.