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.

Define identity element for a binary operation defined on a set.

If G is the set of all matrices of the form [xxxx] , where x in R-{0} , then the identity element with respect to the multiplication of matrices as binary operation, is [1 1 1 1] (b) [-1//2-1//2-1//2-1//2] (c) [1//2 1//2 1//2 1//2] (d) [-1-1-1-1]

A binary operation on a set has always the identity element.

If f:R-R is defined by f(x)=2x+7. Prove that f is a bijection. Also, find the inverse of f .

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.

The number of commutative binary operations that can be defined on a set of 2 elements is

For the binary operation xx_(10) on set S={1,\ 3,\ 7,\ 9} , find the inverse of 3.

If * defined on the set R of real numbers by a*b=(3a b)/7 , find the identity element in R for the binary operation *.

If * defined on the set R of real numbers by a*b= (3a b)/7 , find the identity element in R for the binary operation *.