Let the odd number A multiplied by the odd number B make C.
I say that C is odd.
Since A multiplied by B makes C, therefore C is made up of as many numbers equal to B as there are units in A. And each of the numbers A and B is odd, therefore C is made up of odd numbers, the multitude of which is odd. Thus C is odd.
Therefore, if an odd number is multiplied by an odd number, then the product is odd.