Identity Elements
An identity element is a number which, when combined with a mathematical operation on a number, leaves that number unchanged. For example, the identity element for addition and subtraction is zero, because adding or subtracting zero to a number doesn’t change the number. And zero is also what you get when you add together a number and its opposite, like 3 and -3.
The inverse operation
of addition is subtraction—when you add a number and then subtract that
same number, you end up back where you started. Also, adding a number’s
opposite is the same as subtracting it—for example, 
is the same as 
.
Multiplication and division are also inverse operations to each other—when you multiply by a number and then divide by the same number, you end up back where you started. Multiplication and division also have an identity element: when you multiply or divide a number by one, the number doesn’t change.
Just as the opposite of a number is the number you can add to it to get zero, the reciprocal
of a number is the number you can multiply it by to get one. And
finally, just as adding a number’s opposite is the same as subtracting
the number, multiplying by a number’s reciprocal is the same as dividing
by the number.
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