Question

Let G be the group of all invertible 2 x 2 matrics over the C of complex numbers with matrix multiplication
a)Find the subgroup of G generated by

Answer 1

This matrix. I got you the first time :)
\[\huge \left[\begin{matrix}0 & i \\ i & 0\end{matrix}\right]\]

Answer 2

A=

Answer 3

I have a better handwriting!!!
Just kidding.

So, we're taking a cyclic group, generated by that matrix above, using matrix multiplication.
Evaluate this...\[\huge \left[\begin{matrix}0 & i \\ i & 0\end{matrix}\right]\left[\begin{matrix}0 & i \\ i & 0\end{matrix}\right]\]

Answer 4

If matrices make you dizzy, (they make me dizzy)
use this formula...
\[\huge \left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\left[\begin{matrix}p & q \\ r & s\end{matrix}\right]=\left[\begin{matrix}ap+br & aq+bs \\ cp+dr & cq+ds\end{matrix}\right]\]

Answer 5

looks like we could take out i's