The group of real numbers under multiplication has the identity element:a.-1b.0c.1d.∞

To determine the identity element of the group of real numbers under multiplication, we need to find the number that, when multiplied with any real number, leaves the number unchanged.

Let's consider each option:

a. -1: If we multiply any real number by -1, the result will be the opposite of that number. Therefore, -1 is not the identity element.

b. 0: If we multiply any real number by 0, the result will always be 0. Therefore, 0 is not the identity element.

c. 1: If we multiply any real number by 1, the result will be the same as the original number. Therefore, 1 is the identity element.

d. ∞ (infinity): Infinity is not a real number, so it cannot be the identity element.

Therefore, the correct answer is c. 1.