Key Concepts and Formulas:

1. Determinant of a Product: For square matrices A and B of the same order, $\det(AB) = \det(A)\det(B)$.
2. Zero Matrix Determinant: The determinant of a zero matrix of any order is 0.
3. Invertible Matrix: A square matrix A is invertible (or non-singular) if and only if its determinant $\det(A) \neq 0$. If $\det(A) = 0$, the matrix is singular.
4. Homogeneous System of Linear Equations: For a system $AX=0$ (where $X$ is a column vector of variables and $0$ is a zero column vector):