A fast method of finding determinant

Prerequisite knowledge:
Properties of determinant

For 3x3 determinant:

Prove it yourself or refer to the website below [p6,7].

Examples:
$$\begin{vmatrix}2&4&1\\4&-3&2\\-1&3&-2\end{vmatrix}=\dfrac{1}{2}\begin{vmatrix}-22&0\\10&-3\end{vmatrix}=33$$ $$\begin{vmatrix}4&5&-2\\-7&-4&-5\\-6&2&1\end{vmatrix}=\dfrac{1}{4}\begin{vmatrix}19&-34\\38&-8\end{vmatrix}=\dfrac{19}{2}\begin{vmatrix}1&-17\\2&-4\end{vmatrix}=15\cdot 19=285$$ $$\begin{vmatrix}a+b&a&a\\a&a+b&a\\a&a&a+b\end{vmatrix}=\begin{vmatrix}b&0&-b\\0&b&-b\\a&a&a+b\end{vmatrix}=\dfrac{1}{b}\begin{vmatrix}b^2&-b^2\\ab&b^2+2ab\end{vmatrix}=b^2\begin{vmatrix}1&-1\\a&2a+b\end{vmatrix}=b^2(3a+b)$$

The formula can be generalised as follows:

Reference