# 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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