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A binary operation * is defined on the s...

A binary operation * is defined on the set
`X=R-{-1}` by `x**y=x+y +xy, AA x, y in X`.
Check whether * is commutative and associative. Find its identity element and also find the inverse of each element of X.

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Let A=R xx R and be the binary operation on A defined by (a, b) *(c,d) = (a + c, b + d). Show that *is commutative and associative. Find the identity element for* on A, if any.

If A=N xx N and * is a binary operation on A defined by (a, b) ** (c, d)=(a+c, b+d) . Show that * is commutative and associative. Also, find identity element for * on A, if any.

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.

Let* be a binary operation on Q, defined by a*b= (3ab)/(5) .Show that is commutative as well as associative. Also, find its identity, if it exists.

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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.

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