If \( A=\frac{1}{3}\left[\begin{array}{rrr}1 & 2 & 2 \\ 2 & 1 & -2 ...

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If \( A=\frac{1}{3}\left[\begin{array}{rrr}1 & 2 & 2 \\ 2 & 1 & -2 \\ x & 2 & y\end{array}\right] \) satisfies \( A^{T} A=I \), then \( x+y= \)
(a) 3
(b) 0
(c) \( -3 \)
(d) 1
\( \mathrm{P} \)
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