Constract the composition table/multiplication table for the binary operation * defined on {0,1,2,3,4}by `a**b =axxb ("mod" =5)`. Find the identity element if any. Also find the inverse elements of 2 and 4.

Construct the composition table/multiplication table for the binary operation * defined on {0, 1, 2, 3, 4, 5} given by a**b=ab (mod 6). Find the identity element if any. Also, find the inverse of elements 1 and 5.

For binary operation * defined on 8 -{1}, such that a**b=a+b-ab . Determine the identity element.

Let * is a binary operation on Z defined as a * b = a + b - 5 find the identity element for * on z .

Let be a binary operation defined by a*b = 7a+9b. Find 3*4.

Let * is a binary operation on [0, ¥) defined as a * b = sqrt (a^(2)+b^(2)) find the identity element.

Let S =Q xx Q and let * be a binary operation on S defined by (a, b)* (c,d) = (ac, b+ad) for (a, b), (c,d) in S. Find the identity element in S and the invertible elements of S.

Discuss the commutativity and associativity of binary operation .*. defined on A = Q - {1} by the rule a**b=a-b+ab for all a, b in A . Also, find the identity element of * in A and hence find the invertible elements of A.

Find the identity elements if any for the binary operations defined by a**b=a+b+1,a,b inZ .

Find the identity elements if any for the binary operations defined by a**b=a+b+ab,a,b inQ-{-1} .