Question

Show that the set { 1,-1,i,-i } is closed under multiplication

Answer 1

Answer:

{ 1,-1,i,-i } is closed under multiplication

Step-by-step explanation:

Hi,

Given set , say S = { 1, -1, i, -i}

To show that the given  set 'S' is closed under multiplication, we should show

that for any a, b ∈ S, a*b ∈S

Consider 1 * 1  = 1 ∈ S,

1 * -1 = -1 ∈ S,

Similarly if we do the operation on every pair of numbers from the set S and

enlist them in grid form as shown,

*        1       -1      i      -i

1       1       -1      i      -i

-1      -1       1      -i      i

i         i      -i      -1      1

-i       -i      i       1      -1,

From the above grid of numbers , we can observe that for every pair of

numbers a, b , a* b ∈ S itself,

Hence the given set of numbers are closed under multiplication.

Hope, it helped !