9. Picking out the identity element in a group. (Give me some examples and solve
ID: 3009047 • Letter: 9
Question
9. Picking out the identity element in a group. (Give me some examples and solve them) for example (Z, +) what is the identity element?Another example sym trig the identity:f(x)=x F(X1, x2) = ( x1, x2) why this is the identity? (Give me some more examples and solve them) 9. Picking out the identity element in a group. (Give me some examples and solve them) for example (Z, +) what is the identity element?
Another example sym trig the identity:f(x)=x F(X1, x2) = ( x1, x2) why this is the identity? (Give me some more examples and solve them) 9. Picking out the identity element in a group. (Give me some examples and solve them) for example (Z, +) what is the identity element?
Another example sym trig the identity:f(x)=x F(X1, x2) = ( x1, x2) why this is the identity? (Give me some more examples and solve them)
Explanation / Answer
9. to pick out any identity element in a group
we just have to check whether
any element(let's say x) *(this is your actual operation, whether it be plus , minus, multiply) identity = element
in short for an identity
element * identity = element
with this definition in mind
for (Z, +)
let;s pick up an element 7 + 0 = 7 , so true
let's pick another -9+0 = 9 , so true
so 0 is identity
conversely the shortcut to check is that you just see the operation , here it's + and try to guess what the identity would be . , then try to apply on some real values.
if it is true then ok else, identity does not exist
another example
(Z,*) where * is multiply
obvoiusly let's pick up 1 as our guess since for multiplication it would be nice guess
3*1 = 3 , so true
-9*1 - -9 , again true
hence 1 is identity
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