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.

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 +5 on set S={0,1,2,3,4}

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

Construct the composition table for xx_(5) on Z_(5)={0,1,2,3,4}

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

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

Construct Caley's table for the set {0,1,2,3,4} under multiplication modulo 6.

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