Solution
Given, $$p+\left(\frac{1}{p}\right)=2$$
$$\Rightarrow$$ $$p^2+1=2p$$
$$\Rightarrow$$ $$p^2-2p+1=0$$
$$\Rightarrow$$ $$\left(p-1\right)^2=0$$
$$\Rightarrow$$ $$p-1=0$$
$$\Rightarrow$$ $$p=1$$
$$\therefore\ $$ $$p\times p\times p=1\times1\times1=1$$
Hence, the correct answer is Option C
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