1)
Basic Point:- e * a = a ( where e identity element )
let take bl is left identity and br is right identity
∴ bl * a = a and a * br = a ====> bl * a = a * br ====> where a is an integer, therefore you can cancel them
∴ bl = br
2)
Basic Point:- a-1 * a = e ( where e identity element )
let take bl is left inverse element and br is right inverse element
∴ bl * a = e and a * br = e ====> bl * a = a * br ====> where a is an integer, therefore you can cancel them
∴ bl = br