minor (matrix)

Consider a matrix \[A\],

\begin{align*} A= \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{pmatrix} \end{align*}

Each element in this square matrix has it's own minor. The minor is the value of the determinant of the matrix that results from crossing out the row and column of the element under consideration.
If we were to calculate the minor of \[a\] in \[A\], we would remove \[b\], \[c\], \[d\] and \[e\] to form a matrix:

\begin{align*} \begin{pmatrix} \Box & \Box & \Box \\ \Box & e & f \\ \Box & h & i \\ \end{pmatrix} = \begin{pmatrix} e & f \\ h & i \\ \end{pmatrix} \end{align*}

Then, the minor of \[a\] is \[\det \begin{pmatrix} e&f\\h&i \end{pmatrix}=ei-fh\].

Or if we were to calculate the minor for \[f\], that would be

\begin{align*} \begin{pmatrix} a & b & \Box \\ \Box & \Box & \Box \\ g & h & \Box \\ \end{pmatrix} = \begin{pmatrix} a & b \\ g & h \\ \end{pmatrix} \end{align*}

then the minor of \[f\] is \[\det \begin{pmatrix} a&b\\g&h \end{pmatrix}=ah-bg\].