Question

If g ={1,-1,i,-i} is a group under multiplication, then inverse of g is

Answer 1

Answer:

I'm reading about groups for the first time, and I'm a bit confused as to how to prove that G={1,−1} is a group under multiplication

Answer 2

Answer:

Hence, the inverse of G is:

Inverse of 1 is 1

Inverse of i = -i

Inverse of -1 = -1

Inverse of -i = i

Step-by-step explanation:

I is identity element (e)

        g = {1, -1,i, -i }

Inverse of 1 is 1

Inverse of i = -i

Inverse of -1 = -1

Inverse of -i = i

         

                     $a * a^{-1} = e$

                     1 x 1 = 1

                      i x -i = $-i^{2} = 1$

                     -1 x -1 = 1

                     -i x i = 1

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