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## Main Question or Discussion Point

"Define a * b, for a,b [tex]\in R[/tex] by a * b = ab+a+b. What we just have done is defined a new operation *, in terms of the well known ones multiplication and addition."

Is there a real number which is the identity under the operation * ???

Lets call this number e. A number for which a * e = e * a for all [tex]a \in R[/tex]?

Furtheremore, does every [tex]a \in R[/tex] have an inverse under this operation? ...if so, what could it be?

Is there a real number which is the identity under the operation * ???

Lets call this number e. A number for which a * e = e * a for all [tex]a \in R[/tex]?

Furtheremore, does every [tex]a \in R[/tex] have an inverse under this operation? ...if so, what could it be?