# Math Help - center

1. ## 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?

2. 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.

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.

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

Edited: Sorry, I didn´t see TheArtofSimmetry's post.