### Video Transcript

Which number is the additive
identity for the real numbers? Option (A) negative one, option (B)
zero, or is it option (C) one? Which number is the multiplicative
identity for the real numbers? Option (A) negative one, option (B)
zero, or is it option (C) one?

In the first part of this question,
we need to identify which of three given numbers is the additive identity for the
real numbers. We can begin by recalling what is
meant by an additive identity.

An additive identity is an element
that leaves all of the other elements unchanged after addition. So we are looking for a number 𝑏
that when we add it to any real number 𝑎, we are left with 𝑎. We can recall that adding zero to
any number will leave it unchanged. So zero is the additive
identity. This is given as option (B).

In the second part of this
question, we need to identify the multiplicative identity for the real numbers. We can recall that this is the real
number which when multiplied by any other real number leaves it unchanged. We know that multiplying any real
number by one leaves it unchanged. Hence, the multiplicative identity
of the real numbers is one, which is option (C).

It is also worth noting that the
additive identity and multiplicative identity must be unique. So zero is the only additive
identity of the real numbers and one is the only multiplicative identity of the real
numbers.