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aliases: 
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tags:
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$$
\begin{pmatrix} a & c \\ b & d\end{pmatrix}
\begin{pmatrix}1\\0\end{pmatrix}
=
\begin{pmatrix}1 \\ 0\end{pmatrix}
\iff
\begin{pmatrix}a\\b\end{pmatrix} = \begin{pmatrix}1\\0\end{pmatrix}
$$

$$
\begin{pmatrix} a & c \\ b & d\end{pmatrix}
\begin{pmatrix}0\\1\end{pmatrix}
=
\begin{pmatrix}1 \\ 1\end{pmatrix}
\iff
\begin{pmatrix}c\\ d\end{pmatrix} = \begin{pmatrix}1\\ 1\end{pmatrix}
$$

$P = \begin{pmatrix}1 & 1 \\ 0  & 1\end{pmatrix}$