ABSTRACT MATH: How to show that an operation has no identity? Question shown as in textbook in the description (photo).
It has to do with the concept of algebraic identities, the odd symbol that looks like a multiply is just a binary operation.
It has to do with the concept of algebraic identities, the odd symbol that looks like a multiply is just a binary operation.
1 Answer
Mar 2, 2018
See explanation...
Explanation:
I will use
Given:
#a ox b = a^2b+ab^2#
Suppose
Then:
#a = a ox e = a^2e+ae^2 = a(a+e)e#
Dividing both ends by
#(a+e)e = 1#
Hence:
#a = 1/e-e#
But
Hence we can deduce that there is no such identity