9 Picking out the identity element in a group Give me some e

Solution

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