Answer to Question #117166 in Abstract Algebra for Umar Farouq Aimafal

Question

Let
A
=
l
e
f
t
−
1
,
1
,
−
i
,
i
r
i
g
h
t
,
i
=
s
q
r
t
−
1
.
A=left−1,1,−i,iright,i=sqrt−1. Let the binary operation be multiplication, what is the inverse element of
i
i?

Answer 1

Recall: we can say element a of group G has an inverse if there exist b of group G such that a.b=e ,where 'e' is the identity of group G.

Therefore i has an inverse if there exist an element in A such that it give identity after multiply with i

So, there is an element (-i) in A which give 1 after multiply with i , here 1 is identity of A

So, i.(-i) = - i² =-(-1) = 1

Hence (-i) is an inverse of i

Answer: (-i).