<s>[INST] sum of two determinants If 


\begin{vmatrix}a&c\\b&d\end{vmatrix} and \begin{vmatrix}a&e\\b&f\end{vmatrix}, then sum of these determinant can be written as in terms of another determinant given by
    \begin{vmatrix}a&c+e\\b&d+f\end{vmatrix}


is it right?
 [/INST] The determinant is a multilinear function of its columns and so
$$
\begin{vmatrix}a&c+e\\b&d+f\end{vmatrix}
=\begin{vmatrix}a&c\\b&d\end{vmatrix} + \begin{vmatrix}a&e\\b&f\end{vmatrix}
$$
</s>