Question

i've got a question in my math

its wanting to know why is the 1 called the multiplicative identity

Answer 1

multiplying any number by 1 does not change that number
e.g. 56x1 = 56
the number keeps its "identity".

BTW the "additive" identity would be the number 0

Answer 2

The multiplicative identity is a number, denoted by 1 that has the property that:

1*x = x

for all x


You can then prove that there can only exist one number with this property. If you assume that there are two such numbers 1 and 1', then we have:

1*1' = 1'

because 1 is the identity.

But we also have:


1*1' = 1

because 1' is also the identity. So, we see that 1' = 1 and we see that the multiplicative identity is a unique number.