The equation 1 x 1 = 1 meets the conditions you describe in your question. The whole number 1, when multiplied by itself (1 x 1) yields a product (the result of multiplication) of 1 (the original whole number).
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What is a whole number that can be named as a product of a number with itself?
A perfect square is a whole number that can be named as a product of a number with itself.
It then becomes a square number
A square number.
It is a perfect square.