Question

why do subtraction and division have no identity​

Answer 1

Addition has identity which is zero as x+0=0+x=x, where x is any number.

Multiplication has identity which is 1 as x×1=1×x=x, where x is any number.

Now,

Subtraction does not have identity because x-1 is not equal to 1-x.

E.g. 2-1=1 & 1-2=-1( not equal)

0-x is not equal to x-0.

E.g. 0-2=-2 & 2-0=2(not equal)

Division has no identity because 1÷x is not equal to x÷1.

E.g. 1÷2=0.5 & 2÷1=1(not equal)

0÷2=0 & 2÷0 is not defined.

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