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$\mathrm{AxA} \mathrm{has} 9 \mathrm{elements} \mathrm{implies} \mathrm{that} A \mathrm{has} 3 \mathrm{elements}.$$\mathrm{As} (-1,0) \mathrm{and} (0, 1) \mathrm{are} \mathrm{elements} \mathrm{of} \mathrm{AxA},$$A = \left\{\begin{array}{c}-1, 0, 1\end{array}\right\}$$\mathrm{AxA} =\left\{\begin{array}{c}(-1,-1),\begin{array}{c}(-1,0)\end{array},\begin{array}{c}(-1,1)\end{array},\begin{array}{c}(0,-1)\end{array},\begin{array}{c}(0,0)\end{array},\begin{array}{c}(0,1),\begin{array}{c}(1,-1),\begin{array}{c}(1,0)\end{array},\begin{array}{c}(1,1)\end{array}\end{array}\end{array}\end{array}\right\}$">