$ \LARGE det \begin{bmatrix} \color{black}a & \color{black}a' & \color{black}a'' \\\color{black}b &\color{black}b'&\color{black}b''\\\color{black}c &\color{black}c'&\color{black}c'' \end{bmatrix} = ab'c'' + a'b''c + a''bc' - cb'a''- c'b''a-c''ba'$

Got it !

Determinante einer Matrix 3 x 3

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$ \LARGE det \begin{bmatrix} \color{black}1 & \color{black}1 & \color{black}-3 \\\color{black}1 &\color{black}0&\color{black}1\\\color{black}-1 &\color{black}2&\color{black}1 \end{bmatrix} = $	$\LARGE 0 - 1 - 6 - 0 - 2 - 1 = -10$
$ \LARGE det \begin{bmatrix} \color{black}1 & \color{black}2 & \color{black}3 \\\color{black}0 &\color{black}4&\color{black}5\\\color{black}0 &\color{black}0&\color{black}6 \end{bmatrix} = $	$\LARGE 24 + 0 + 0 - 0- 0 - 0 = 24 $
$ \LARGE det \begin{bmatrix} \color{black}1 & \color{black}0 & \color{black}0 \\\color{black}0 &\color{black}1&\color{black}0\\\color{black}0 &\color{black}0&\color{black}1 \end{bmatrix} = $	$\LARGE 1 + 0 + 0 - 0 - 0 - 0 = 1$