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The Same Variable Matrices in Matrix Thereom states that:


<math>
\begin{bmatrix}
\begin{bmatrix}
a & c\\
b & d
\end{bmatrix} & \begin{bmatrix}
c & a\\
b & d
\end{bmatrix}\\
\begin{bmatrix}
a & c\\
d & b
\end{bmatrix} & \begin{bmatrix}
c & a\\
d & b
\end{bmatrix}
\end{bmatrix}
= 4abcd - {ab}^2 - {bc}^2 - {cd}^2 - {ad}^2
</math>

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