" Find the identity element in the set "I^(+)" of all positive integers defined by "a*b=a+b" for all "

Find the identity element in set Q^+ of all positive rational numbers for the operation * defined by a*b= (a b)/2 for all a , b in Q^+dot

Find the identity element in set Q^+ of all positive rational numbers for the operation * defined by a*b=(a b)/2 for all a , b in Q^+dot

Find the identity element in set Q^(+) of all positive rational numbers for the operation * defined by a^(*)b=(ab)/(2) for all a,b in Q^(+)

For each binary operation * defined below, determine the identity element. On Q^(+) , all positive rational numbers defined by a*b= (ab)/(2) .

let ** be a binary operation on ZZ^(+) , the set of positive integers, defined by a**b=a^(b) for all a,binZZ^(+) . Prove that ** is neither commutative nor associative on ZZ^(+) .

Find the identity element in the set of all rational numbers except -1 with respect to * defined by a*b= a+b+a b .

Find the identity element in the set of all rational numbers except -1 with respect to * defined by a*b=a+b+ab

Find the identity element of the binary operation ** on ZZ defined by a**b=a+b+1 for all a,binZZ .

Let * be a binary operation on the set Q_0 of all non-zero rational numbers defined by a*b= (a b)/2 , for all a ,\ b in Q_0 . Show that (i) * is both commutative and associative (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

If ** be the binary operation on the set ZZ of all integers, defined by a**b=a+3b^(2) , find 2**4.