Here say ,
S=$\left \{ 0,1,2,3,4 \right \}$
the group is defined as (S,$+_{5}$).
Here identity element is 0.
So we have find inverse of 2.
say inverse of 2 is x.
so , 2$+_{5}$x=0
now what do you think which of the group element suffice this condition true ?
it is 3 as (2+3) mod 5=0 .
so inverse of 2 is 3.
now we have to find $2^{-3}=(2^{-1})^{3}=3^{3}=(3+3+3)mod 5=4$
By going through the same process we can also conclude that inverse of 3 is 2.
so ,$3^{-2}=(3^{-1})^{2}=2^{2}=(2+2)mod 5=4$
correct answer is option C.
