This is because anything squared is always positive. For example: 1 times 1= 1 and (-1) times (-1)= 1. The only number that when squared will give you a negative number are irrational, such as i. i is equal to the square root of (-1).
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Well, sweetheart, when you multiply a number by itself, you're essentially squaring it. And no matter how many times you square a real number, you'll always end up with a positive result. It's just the way the math cookie crumbles. So, in short, the product of an integer multiplied by itself can never be negative because math said so.
When an integer is multiplied by itself, the result is always a positive number or zero. This is because a negative number multiplied by a negative number results in a positive number, and a positive number multiplied by a positive number is also positive. Therefore, the product of an integer multiplied by itself can never be negative due to the properties of multiplication and the concept of positive and negative numbers.
The smallest positive integer is 1. 1 is the multiplicative identity; ie anything times 1 is itself. The greatest negative integer is the most positive negative integer which is -1. Therefore the product of the greatest negative integer and the smallest positive integer is the greatest negative integer which is -1.
An Exponent.
There are just three possible cases: Positive integer: positive x positive = positive. Negative integer: negative x negative = positive. Zero: zero x zero = zero.
The product is a perfect square.
It'd be the product squared, since you're multiplying it by itself. the product of a number multiplied by itself is called an Exponent, Power or Square Number