This concept establishes the fundamental rule for computing determinants in linear algebra through cofactor expansion or direct product differences applied exclusively to second-order square matrices. The theory relies on formal definitions regarding matrix elements, minors, and the sign convention (checkerboard pattern) used to determine whether a system possesses unique solutions based on non-singularity. It operates within the domain of finite-dimensional vector spaces as a specific analytical mechanism for evaluating scalar values intrinsic to 2x2 square matrices without invoking generalized row reduction techniques.
Prerequisite chain context: requires Homogeneous Systems of Linear Equations in Math.