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.

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} .

Construct the composition table for +_5 on set S={0,\ 1,\ 2,\ 3,\ 4} .

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.

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

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

On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity element for the multiplication of matrices as a binary operation. Also, find the inverse of an element of M.

On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity element for the multiplication of matrices as a binary operation. Also, find the inverse of an element of M.

Find the identity element for the binary operation * on Z defined as a*b = a + b-5. Also find the inverse element of 100.

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