- #1
roam
- 1,271
- 12
"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?