let S denote the set of all ordered pairs of real numbers. For any pair alpha=(asub1,asub2),beta=(bsub1,bsub2) of element of S define
alpha+beta=(asub1+bsub1,asub2+bsub2)
alpha*beta=(asub1bsub1+3asub2bsub2,asub2bsub1+asub1bsub2)
determine whether or not S is a field together with these operations for addition and multiplication.If so, prove that all the conditions in the definition of a field are satisfied,If not, show that at least one condition does not hold.

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Multiplicative inverse is not looking good...... or maybe I'm just tooooo rusty at this, lol.

it's really too hard isn't it? that's why i need someones help =)

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