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The identity element for the binary oper...

The identity element for the binary operation `**` defined on Q - {0} as `a ** b=(ab)/(2), AA a, b in Q - {0}` is

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Find the identify element for the binary operation *, defined on the set of Q of rational number, by a * b =(ab)/(4)

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Knowledge Check

  • Binary operation * on R - {-1} defined by a * b= (a)/(b+a)

    A
    * is associative and commutative
    B
    * is neither associative nor commutative
    C
    * is commutative but not associative
    D
    * is associative but not commutative

  • Binary operation * on R -{-1} defined by a ** b = (a)/(b+1) is

    A
    * is associative and commutative
    B
    * is associative but not commutative
    C
    * is neither associative nor commutative
    D
    * is commutative but not associative

  • The inverse of 2010 in the group Q^(+) od all positive rationals under the binary operation * defined by a^(**)b=(ab)/(2010),AAa,binQ^(+) , is

    A
    2011
    B
    2009
    C
    2010
    D
    1

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    Let * be a Binary operation defined on N by a ** b = 2^(ab) . Prove that * is commutative.

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