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).