- #1
PsychonautQQ
- 784
- 10
Homework Statement
Let ab=a and ba=b, show that a^2 = a and that b^2 = b
Homework Equations
none
The Attempt at a Solution
Not sure if I did this correct.. but here is what I did.
Given:
ab = a. Multiply both by left hand multiplication by a^-1
a^-1*a*b = 1. where a^-1*a is obviously the identity.
so b = 1.
Given:
ba = b. Multiply both by left hand multiplication by b^-1.
b^-1*b*a = 1
1a=1
a=1
so a =1.
If b = 1 and a=1, then b^2 = 1 and a^2 = 1, so a^2 = a and b^2 = 2. Did I do this correctly?