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Home » Let be the set of four 4 th roots of unity. Prepare the composition table for multiplication on and show that (iii) multiplication is commutative on A, (iv) 1 is the multiplicative identity,
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 (iii) multiplication is commutative on A, (iv) 1 is the multiplicative identity,
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 (iii) multiplication is commutative on A, (iv) 1 is the multiplicative identity,

(iii)

For commutative, \mathrm{a} \times \mathrm{b}=\mathrm{b} \times \mathrm{a}

\begin{array}{l} 1 \times-1=-1 \\ -1 \times 1=-1 \end{array}

\mathrm{a} \times \mathrm{b}=\mathrm{b} \times \mathrm{a}, so \mathrm{A} is commutative for multiplication.

(iv)

For multiplicative identity element e, ax e =ex a = a where a \in A.

\begin{array}{l} a \times e=a \\ a(e-1)=0 \end{array}

either a=0 or e=1 as a \neq 0 hence e=1

So, multiplicative identity element \mathrm{e}=1 .

i

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