- #1

Oxymoron

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**Question**

Let [itex]G=GL(2,\mathbb{R})[/itex] be the group of invertible [itex]2\times 2[/itex] martrices with real entries. Consider the action of [itex]G[/itex] on itself by conjugation. For the element

Let [itex]G=GL(2,\mathbb{R})[/itex] be the group of invertible [itex]2\times 2[/itex] martrices with real entries. Consider the action of [itex]G[/itex] on itself by conjugation. For the element

[tex]A= \left(\begin{array}{cc}

2 & 1 \\

0 & 3

\end{array}\right)[/tex]

**of**[itex]G[/itex]

**, describe (i) the orbit and (ii) the isotropy group of**[itex]A[/itex]

Sorry, I have no working out because I am completely stumped. Can anyone give me some helpful hints or pointers. Thanks