Determinant Calculator
Compute the determinant of any square matrix (up to 6×6) using cofactor expansion — with full step-by-step breakdown of each minor and sign pattern.
Matrix Setup
How Cofactor Expansion Works
Cofactor Expansion (Laplace Expansion): For an n×n matrix A, expanding along the first row:
$$\det(A) = \sum_{j=1}^{n} (-1)^{1+j} \cdot a_{1j} \cdot M_{1j}$$
where $M_{1j}$ is the minor obtained by deleting row 1 and column j. The sign pattern follows $(-1)^{i+j}$:
$$\begin{pmatrix} + & - & + & \cdots \\ - & + & - & \cdots \\ + & - & + & \cdots \end{pmatrix}$$