Let \( A=N \times N \). Define \( * \) on \( A \) by \( \mathrm{P} ...

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Let \( A=N \times N \). Define \( * \) on \( A \) by
\( \mathrm{P} \) \( (a, b) *(c, d)=(a+c, b+d) \).

W
Show that
\( A \) is closed for *,
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