Determinants of Matrices
Table of Contents
The determinant of a matrix is a scalar value that can be calculated from the elements of the matrix. It is denoted by \(\small \det(A)\) or \(\small |A|\).
$$ \det\begin{bmatrix}\ a & b\\ c & d\\ \end{bmatrix}=ad-cb $$
$$\det\begin{bmatrix} a & b & c\\ d & e & f\\ g & h & i \end{bmatrix}=a\begin{vmatrix} e & f\\ h & i \end{vmatrix}-b\begin{vmatrix} d & f\\ g & i \end{vmatrix}+c\begin{vmatrix} d & e\\ g & h \end{vmatrix}$$
The pattern continues for larger matrices, here is an example of a 4x4 matrix determinant by Byju’s.