Question

Need help understanding the concept. Please.

Answer 1

it is worked out for you
you have to check
closed
associative
there is an identity
each element has an inverse

Answer 2

I don't understand the last paragraph :Check that the number 2 acts as the multiplicative identity,and if ais nonzero, then 4 /a is a nonzero rational number that serves as the multiplicative inverse of a
.

Answer 3

you have to check that \[a\star 2=a\]

Answer 4

and how 4/a is a multiplicative inverse of a?

Answer 5

did you check that \(a\star2=2\star a=a\) ?

Answer 6

they have to equal 1 ?

Answer 7

@xapproachesinfinity no, 1 is not the identity!

Answer 8

Oh, I got it. :) thank you very much.

Answer 9

2 is because \[a\star 2=\frac{2a}{2}=a\]

Answer 10

isn't multiplication identity 1?

Answer 11

ok good
you only need to check now that
\[a\star\frac{4}{a}=2\] which it is

Answer 12

One more question: is there any clue to find that identity?

Answer 13

besides the fact that you were told?

Answer 14

yes, solve \[a\star e=a\] for \(e\)

Answer 15

Oh, yyyyyyes! again, thank you

Answer 16

you get
\[a\star e=\frac{ae}{2}=a\] solve for \(e\) gives \(e=2\)

Answer 17

yw