Solving Part B of a Math Problem: Can You Help?

[Mattofix]

Homework Statement

http://img88.imageshack.us/img88/3148/scan0001ba3.th.jpg

Homework Equations

The Attempt at a Solution

I have done part a, proving the four axioms. I just don't understand part b) if someone could point me in the right direction...

 

[Dick]

Suppose g=[a b,0 d] (I hope the informal matrix notation is clear) is in the center. That means for ANY g'=[a' b',0 d'] in the group, that g*g'=g'*g. Write that out in components. You should find a*b'+b*d'=a'*b+b'*d. Now since the primed components are arbitrary, what does this imply for g if you pick say, a'=1, b'=0 and d'=0. Or if you pick a'=0, b'=1 and d'=0?

 

[Mattofix]

a = d , b = 0 ?

 

[Mattofix]

...so Z(G) = ( a 0 ,0 a ) ?

 

[HallsofIvy]

Does that say "Z(G)= {g | gh= hg for all h}"? The lower bar of the "=" is very pale and it looks like "gh- hg" which makes no sense!

 

[Mattofix]

yes it does - strange though, shows up fine on my screen

 

[Mattofix]

a quick reply would be much appreciated as i have to hand this in pretty soon

 

[Dick]

a quick reply would be much appreciated as i have to hand this in pretty soon

Yes, the center is the multiples of the identity.

 

[Mattofix]

thanks