Matrix Determinant Calculator

The determinant is a scalar value computed from a square matrix. It tells you whether the matrix is invertible and describes the scaling factor of the linear transformation.

2×2 Matrix: det = ad − bc For matrix [[a, b], [c, d]]

3×3 Matrix (cofactor expansion along first row): det = a(ei − fh) − b(di − fg) + c(dh − eg) For matrix [[a, b, c], [d, e, f], [g, h, i]]

Key properties:

• If det = 0, the matrix is singular (not invertible)
• If det ≠ 0, the matrix is invertible
• det(AB) = det(A) × det(B)
• Swapping two rows negates the determinant