Can 0 be the identity for multiplication? Explain why or
why not.
Let e be an identity element under the operation •, then by definition, for all elements a of the group of real numbers,
e•a = a•e = a ....(1)
If we take • as multiplication ×, and 0 as e, the identity element, can we say:
0×a = a×0 = a ?
If not, 0 is not the identity element.
What number e do you think will satisfy the above relationship (1), or
e × a = a × e = a?