Compute the determinant of square matrices up to 4x4 using cofactor expansion or Gaussian elimination. Step-by-step solutions with visualization.
The determinant of a square matrix is a scalar value that can be computed from the matrix's elements. It provides important information about the matrix, such as whether it is invertible (non-zero determinant) and the scaling factor for volumes in linear transformations.
This calculator supports matrices up to 4x4 and uses cofactor expansion (Laplace formula) for exact computation. For larger matrices, Gaussian elimination (row reduction) is more efficient. The determinant is 0 if the matrix is singular (rows/columns are linearly dependent).
Note: Determinant = 0 means the matrix is singular (not invertible).
Expand along a row or column using cofactors. det(A) = Σ a_ij * C_ij where C_ij is the cofactor.
Row reduction to triangular form. det = product of diagonal elements (sign changed for row swaps).