4×4 Matrix Determinant Calculator

About this calculator

The determinant of a square matrix is a single number that reveals key properties of the linear transformation it represents — a determinant of zero means the matrix is singular (not invertible, and its rows/columns are linearly dependent), while a nonzero determinant means it's invertible. For a 4×4 matrix, expanding by cofactors directly requires 4! = 24 terms, so it's far more efficient to use Gaussian elimination with partial pivoting, reducing the matrix to upper-triangular form and multiplying the diagonal entries (tracking sign flips from row swaps).

This calculator takes all 16 entries of your 4×4 matrix, runs Gaussian elimination to compute the determinant, and tells you whether the matrix is singular or invertible. It's a standard tool for linear algebra students and anyone working with linear systems, computer graphics transformations, or engineering models who need to check invertibility before solving a system or inverting a matrix.