User:Emobeam/sandbox

$$ \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} \begin{pmatrix} p & q \\ r & s \\ t & u \end{pmatrix} = \begin{pmatrix} a_ {11} & a_ {12} \\ a_ {21} & a_ {22} \end{pmatrix} $$ $$ det \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad-bc $$ $$ A^ {-1}=\frac{1}{det A} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} = \frac{1}{ad-bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix} $$ $$ \begin{pmatrix} 3 & -4 \\ -2 & 5 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -27 \\ 25 \end{pmatrix} $$