SOLUTION: The binary operation * is defined on real numbers as follows. A*b = a + b- ab where a , b € real numbers. A) show that there is an identity element with respect to *. B) find

Algebra ->  Distributive-associative-commutative-properties -> SOLUTION: The binary operation * is defined on real numbers as follows. A*b = a + b- ab where a , b € real numbers. A) show that there is an identity element with respect to *. B) find      Log On


   

Question 999114: The binary operation * is defined on real numbers as follows.
A*b = a + b- ab where a , b € real numbers.
A) show that there is an identity element with respect to *.
B) find the inverse for each element.
C) show that * is commutative.
D) solve a * ( a*2) = 10.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Not any A, but just a and b for the model.

Only doing identity element part.

Let e be identity element.
a*e=a+e-ae=a
a+e-ae=a
e-ae=a-a
e-ae=0
e(1-a)=0
e=0/(1-a)
e=0

The expression e*a should also be tested, but the identity element e seems to be the same as 0.