Find the inverse of any 2×2 to 6×6 matrix using Gauss-Jordan elimination with partial pivoting. Get the determinant, trace, rank, Frobenius norm, and every row operation shown step by step.
Enter a square matrix — must be non-singular (det ≠ 0)
VERIFICATION — A × A⁻¹ should equal Identity Matrix I
Augmented matrix [A | I] reduced to [I | A⁻¹] via row operations. Orange = pivot column.
Value Heatmap
Input matrix values
2×2 Inverse
A⁻¹ = (1/det) × adj(A)
2×2 Determinant
det = ad − bc
Gauss-Jordan
[A|I] → rref → [I|A⁻¹]
Verification
A × A⁻¹ = A⁻¹ × A = I