Login/Sign Up
Home » Let be the set of four 4 th roots of unity. Prepare the composition table for multiplication on and show that (i) A is closed for multiplication, (ii) multiplication is associative on ,
Let A=(1,-1, i,-i) be the set of four 4 th roots of unity. Prepare the composition table for multiplication on \mathrm{A} and show that (i) A is closed for multiplication, (ii) multiplication is associative on \mathrm{A},
Binary Operations | CBSE | Class 12 | Exercise 3B | Maths | RS Aggarwal
Let A=(1,-1, i,-i) be the set of four 4 th roots of unity. Prepare the composition table for multiplication on \mathrm{A} and show that (i) A is closed for multiplication, (ii) multiplication is associative on \mathrm{A},

(i)

A is said to be closed on * if all the elements of a^{*} b \in A. composition table is

\left(\text { as } i^{2}=-1\right)

As table contains all elements from set A, A is close for multiplication operation.

(ii)

For associative, \mathrm{a} \times(\mathrm{b} \times \mathrm{c})=(\mathrm{a} \times \mathrm{b}) \times \mathrm{c}

\begin{array}{l} 1 \times(-i \times i)=1 \times 1=1 \\ (1 \times-i) \times i=-i \times i=1 \end{array}

\mathrm{ax}(\mathrm{b} \times \mathrm{c})=(\mathrm{a} \times \mathrm{b}) \times \mathrm{c}, so

\mathrm{A} is associative for multiplication.

i

More Material