Prepare the composition table for multiplication `(xx)` on the set of fourth roots of unity and discuss its important properties.

Find the fourth roots of unity.

Let S={1,omega,omega^(2)} be the set of cube roots of unity. Prepare the composition table for multiplication (xx) on S, show that multiplication on S is a binary operation and it is commutative on S. Also, show that every element on S is invertible.

Prepare the composition table for multiplication modulo 6 (xx_(6)) on A={0,1,2,3,4,5}.

Let A={1,-1,I,-i} be the set of fourth roots of unity. Prepare the composition table for multiplication (xx) on A . Show that multiplication on A. Find the identity element for multiplication and show that every element of A is invertible.

Let A={1,omega,omega^(2)} be the set of cube roots of unity. Prepare the composition table for multiplication (xx) on A. Show that multiplication on A is a binary operation and it is commutative on A. Find the identity element for multiplication and show that every element of A is invertible.

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.

Consider the set S={1,\ -1} of square roots of unity and multiplication (xx) 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.

An operation ** is defined on the set S={1,2,3,5,6} as follows: a**b=ab(mod7) Construct the composition table for operation ** on S and discuss its important properties.

Write the multiplication table for the set of integers modulo 5.