A summary:
Since no number can be multiplied by zero to give us one, and since nothing else can, we can safely say that:
Code:Nothing multiplied by zero equals one.
To falsify this we must show either that:
Code:1. There is a number that multiplied by zero equals one.
2. There is something else, other than a number, that:
(a) can be multiplied at least by zero -- as indeed there is:
a matrix -- which is not a number -- can be multiplied not only by zero,
but also by any other number.
(b) in being multiplied by zero, results in one -- which there isn't:
a matrix, if multiplied by zero, does not result in one,
nor does it any other mathematical object.
So, since 1) no number multiplied by zero equals one, since 2) no matrix or any other mathematical object can be multiplied by zero to give us one, and since 3) no non-mathematical object can even be multiplied by zero or any other number, we can only conclude that:
Nothing multiplied by zero equals one.
By saying this is false, we are saying
at least one of the following:
1) There is a number that multiplied by zero equals one.
2) There is another mathematical object than a number that multiplied by zero equals one.
3) There is a non-mathematical object that multiplied by zero equals one.
Each one of which is false, for the already given reasons.