Originally Posted by

**MichaelMath** I'm having a little trouble with the difference between my notes and my textbook notation.

I have

$\displaystyle a = \[ \left( \begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array} \right)\] $

$\displaystyle b = \[ \left( \begin{array}{cc} i & 0 \\ 0 & -i \end{array} \right)\] $

I have to determine the orders of $\displaystyle \left< a \right>$ and $\displaystyle \left< b \right>$, and whether $\displaystyle \left< a \right>$ and $\displaystyle \left< b \right>$ are isomorphic.

For the first part I have $\displaystyle a^4=b^4=I_2$

So they have order 4. Correct?

Yes, but also because 4 is the minimal natural power to which both matrices are I

For the isomorpic part can I just find a 2x2 matrix that shows that $\displaystyle a \rightarrow b$ isn't a homomorphism?

Do I even know what I'm talking about? (just started group theory last week)