If the product of two whole numbers is 1, can we say that one or both of them will be 1?

If the product of two whole numbers is 1, can we say that one or both of them will be 1? Justify through examples.

We know that if a is any whole number, then
a x 1 = a -1 x a
∴ Clearly a must be = 1
Thus, both the numbers should be 1 i. e., 1 x 1 = 1