Dit lijkt me gewoon niet te kloppen hoor.
[latex]
\begin{eqnarray}
\left( \begin{array}{c}
\pi_{1}~A \\
\pi_{2}~B \end{array} \right) =
\left( \begin{array}{cc}
q_{11} & q_{12} \\
q_{21} & q_{22}\end{array} \right)^{-1}
~\left( \begin{array}{c}
X \\
Y \end{array} \right) \\
\left( \begin{array}{cc}
\frac{1}{A} & 0 \\
0 & \frac{1}{B}\end{array} \right)
\left( \begin{array}{c}
\pi_{1}~A \\
\pi_{2}~B \end{array} \right) =
\left( \begin{array}{cc}
\frac{1}{A} & 0 \\
0 & \frac{1}{B}\end{array} \right)
\left( \begin{array}{cc}
q_{11} & q_{12} \\
q_{21} & q_{22}\end{array} \right)^{-1}
~\left( \begin{array}{c}
X \\
Y \end{array} \right) \\
\left( \begin{array}{c}
\pi_{1} \\
\pi_{2} \end{array} \right) =
\frac{1}{det(Q)}
\left( \begin{array}{cc}
\frac{1}{A} & 0 \\
0 & \frac{1}{B}\end{array} \right)
\left( \begin{array}{cc}
q_{22} & -q_{12} \\
-q_{21} & q_{11}\end{array} \right)
~\left( \begin{array}{c}
X \\
Y \end{array} \right)\\
\not=
\frac{1}{det(Q)}
\left( \begin{array}{cc}
q_{22} & -q_{12} \\
-q_{21} & q_{11}\end{array} \right)
\left( \begin{array}{cc}
\frac{1}{A} & 0 \\
0 & \frac{1}{B}\end{array} \right)
~\left( \begin{array}{c}
X \\
Y \end{array} \right)
\end{eqnarray}
[/latex]
Heb je niet toevallig een voorbeeld gebruikt dat wel klopt?
Of zie ik hier iets over het hoofd?