Determinant Calculator
Compute the determinant of any square matrix. Uses cofactor expansion for matrices up to 5×5 (with full step-by-step minors) and row reduction for larger matrices.
Input Matrix
×3
Examples
Result
Enter a square matrix and click Compute Determinant
Cofactor Expansion
For small matrices (up to 5×5), we expand along the first row, computing each minor determinant recursively. This shows the full algebraic structure.
Row Reduction
For large matrices, row reduction to upper triangular form is more efficient. The determinant is the product of diagonal entries, adjusted for row swaps.
Properties
det(AB) = det(A)det(B). Swapping rows negates the determinant. A zero determinant means the matrix is singular (not invertible).