#GroupTheory #TestBook

Question

Plz explain this question

Answer 1

For existence identity element 'e' : 

x op  e  =  e op  x   =    x

Here    x  op   y      =    x + y - 2

 So      x  op e        =    x + e - 2   =  x  [ As mentioned above ]

                             ==> e  =  2

Now  e op x should also yield the same identity element , else identity element does not exist..

So     e op  x         =    e + x -  2    =   x

                            ==>  e  =  2

Hence in both cases we get e = 2 and hence 2 is the required identity element..

Now for finding inverse , say y w.r.t x :

         x op  y       =    e

==>   x + y - 2     =    2

==>   y                =    4 - x

Hence C) should be the correct answer..