Consider the set `S={1,\ -1}` of square roots of unity and multiplication `(xx)` as a binary operation on `Sdot` Construct the composition table for multiplication `(xx)` on `Sdot` Also, find the identity element for multiplication on `S` and the inverses of various elements.

Construct the composition table for +5 on set S={0,1,2,3,4}

Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity. Construct the composition table for multiplication (xx) on Sdot Also, find the identity element for multiplication on Sdot Also, check its commutativity and find the identity element. Prove that every element of S is invertible.

Construct the composition table for xx_(4) on set S={0,1,2,3}.

Consider the set S={1,-1,i,-i} of fourth roots of unity.Construct the composition table for multiplication on S and deduce its various properties.

Consider the set S={1,-1,i ,-1} for fourth roots of unity. Construct the composition table for multiplication on S and deduce its various properties.

Construct the composition table for xx_6 on set S={0,\ 1,\ 2,\ 3,\ 4,\ 5} .

Let * be an associative binary operation on a set S with the identity element e in S. Then. the inverse of an invertible element is unique.

On the set M=A(x)={[[x,xx,x]] : x in R} of 2x2 matrices,find the identity element for the multiplication of matrices as a binary operation.Also,find the inverse of an element of M.

Write the composition table for the binary operation multiplication modulo 10(xx_(10)) on the set S={2,4,6,8}

Write the composition table for the binary operation xx5 (multiplication modulo 5) on the set S={0,1,2,3,4}.