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Group theory matrix question

Group theory matrix question

nohomo

Show that there is a largest multiplicative group of 2x2 matrices with real entries containing

\begin{bmatrix}0 & 0 \\ 5 & -5\end{bmatrix}

and find this group

Reply 1

DFranklin

For ease, call that matrix A.

It might help to think about the action of A on the a general 2x2 matrix. Since you're going to need to be able to invert A, you need to exclude anything that gets mapped to 0. That should give you an idea what's going on.

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