Math

A binary operation * is defined on the set R of real numbers by: a+b+ab where a, b€R .Calculate 5*(-2)*5.Find the identity element of R under the operation*. Determine the inverse under * of a general element a €R

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  1. I shall assume that * associates left to right, like addition. If so, then
    5*(-2)*5 = (5*(-2))*5 = (5 + -2 + 5(-2))*5 = (-13)*5
    = -13 + 5 + (-13)(5) = -73

    What is the identity element under *? It must be zero, since a*0 = a
    If b = a-1 under * then a*b = b*a = 0
    So, what do you think a-1 is?

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    oobleck
  2. oops. 5*-2 = -7
    fix the 2nd step.

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    oobleck
  3. Respond

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  4. This is another way to solve it:
    2.b = a + b + ab where a, b ER
    5.(-2).5
    solution
    5+(-2)=5+(-2)+5X(-2)
    = 5-2-10
    = 3-10 =-7
    (-7).5=- 7+5+(-7) 5
    = 7+5 35
    =-2-35
    =-37

    (ii) a. era
    ate+aera
    etae = a-a
    e(1+a)=0

    e = 0

    Let a' be the inverse of a, then

    ata' + aa' = 0
    a' taa' =-a
    a'(1+a)=-a

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