(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider this group of six matrices:

Let G = {I, A, B, C, D, K}, Matrix Multiplication>

[tex]I =\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}[/tex] [tex]A =\begin{bmatrix}0 & 1\\1 & 0\end{bmatrix}[/tex] [tex]B =\begin{bmatrix}0 & 1\\-1 & -1\end{bmatrix}[/tex]

[tex]C =\begin{bmatrix}-1 & -1\\0 & 1\end{bmatrix}[/tex] [tex]D =\begin{bmatrix}-1 & -1\\1 & 0\end{bmatrix}[/tex] [tex]K =\begin{bmatrix}1 & 0\\-1 & -1\end{bmatrix}[/tex]

Operation Table for this group:

_|I A B C D K

I |I A B C D K

A|A I C B K D

B|B K D A I C

C|C D K I A B

D|D C I K B A

K|K B A D C I

Define [tex] f:G\rightarrow[/tex] [tex]\left\langle\(R^{*}, \bullet\right\rangle[/tex] by f(x) = det(x) for any Matrix x [tex]\in[/tex] G.

Finally, the question. Haha.

Find all the conjugates of A:

Find all the conjugates of B:

2. Relevant equations

N/A

3. The attempt at a solution

Now I know this isn't that hard of a concept and I understand what a conjugate is but I don't know how to find them. Any help on how I would go about finding them is greatly appreciated.

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# Abstract Algebra: Finding Conjugates

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