Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Apne doubts clear karein ab Whatsapp par bhi. Try it now.

CLICK HERE

Watch 1000+ concepts & tricky questions explained!

50.8 K+

2.5 K+

Text Solution

Answer :

(i)0 (ii) `a^(-1)=(a)/(a-1)` Solution :

(i) Let e be the identity element Then for all a in Q-{1} we have <br> `a*e=a rarr a+e-ae=a` <br> `rarr e(1-a=0 rarr e=0` [before a `ne` 1] <br> `therefore` 0 is the identity element <br> (ii) Let a in Q-{1} be an arbitray element and let b be its inverse <br> Then `a*b=0 rarr a+b-ab=0 rarr ab-b=a` <br> `rarr b(a-1)=a rarr b=(a)/(a-1)` <br> Thus each a in Q-{1} has `(a)/(a-1)` as its inverse