# center

• Feb 26th 2011, 03:59 AM
alexandrabel90
center
how do you find the center of a 2x2 matrix group where elements all have det + 1 or -1.

isit -I and I?

what about the center when the determinant of the elements in the group all have det=1?
• Feb 26th 2011, 04:38 AM
TheArtofSymmetry
Quote:

Originally Posted by alexandrabel90
how do you find the center of a 2x2 matrix group where elements all have det + 1 or -1.

isit -I and I?

Assume your matrix group is over the field K. Then, the center consists of all scalar matrices whose determinant is 1 or -1.

Quote:

what about the center when the determinant of the elements in the group all have det=1?
Similarly, the center consists of all scalar matrices whose determinant is 1.

In this case, the center is isomorphic to the group of n-th roots of unity in K.

Edit: In this case, just n=2.
• Feb 26th 2011, 04:38 AM
FernandoRevilla
For both groups, the center is \$\displaystyle Z=\{I,-I\}\$ .

Edited: Sorry, I didnīt see TheArtofSimmetry's post.