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?

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- Feb 26th 2011, 03:59 AMalexandrabel90center
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 AMTheArtofSymmetry
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?

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 AMFernandoRevilla
For both groups, the center is $\displaystyle Z=\{I,-I\}$ .

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