Question

This is a valid way of finding a determinant of a matrix right:
(cause it didn't work for me)

Answer 1

\[\det(\left[\begin{matrix}a & b & c \\ d & e & f \\ g & h & i\end{matrix}\right]) = a*\det(\left[\begin{matrix}e & f \\ h & i\end{matrix}\right]) - d*\det(\left(\begin{matrix}b & c \\ h & i\end{matrix}\right)) + g*\det(\left[\begin{matrix}b & c \\ e & f \end{matrix}\right])\]

Basically you pick the left-most column, take out the coefficient and multiply it by the cofactor.

I used exactly this formula for a matrix with a column of a single 1, and the rest are 0s, but they didn't turn out to be the same. So I want to be clear that this method of finding a determinant is correct.

Answer 2

OMG I DID A MISCALCULATION I AM AN DIIOTTTTTTT