2×2 / 3×3 Matrix Calculator

A matrix inverse gets used to solve systems of linear equations, and by hand it means a page of cofactor arithmetic where one sign error anywhere invalidates the whole answer. Matrix Calculator runs the same cofactor-expansion method for 2×2 and 3×3 matrices instantly, alongside addition, subtraction, multiplication and transpose.

Reach for it to check homework by hand, verify a linear algebra step in a larger calculation, or get a quick determinant without opening a full computer algebra system. Switch between 2×2 and 3×3 at any time; changing size resets both matrices to zero.

Running Your First Matrix Operation

1. Pick 2×2 or 3×3 under Size.
2. Type values into Matrix A, and Matrix B too if you’ve picked A + B, A − B or A × B.
3. Choose an Operation. det(A) and A⁻¹ only look at Matrix A, so the second grid disappears when either is selected.

How the Math Works: Determinant and Inverse

The 2×2 determinant is ad − bc; the 3×3 case expands along the first row into three 2×2 determinants with alternating signs. The inverse is the adjugate matrix (the cofactor matrix, transposed) divided by the determinant — the standard method taught in a first linear algebra course. Every formula here was checked during development against NumPy’s linalg.det and linalg.inv on two test matrices and matched exactly, including a 3×3 case with a determinant of exactly 1.

Edge Cases: Singular Matrices and Rounding

A matrix with a determinant of 0 has no inverse by definition — [[1,2],[2,4]] is the simplest example, since its second row is just the first row doubled. Clicking A⁻¹ on a matrix like that shows “Matrix is singular (determinant = 0) — it has no inverse.” rather than dividing by zero silently. Results are rounded to 4 decimal places for display, so an inverse that’s mathematically exact may show a value like 0.3333 instead of the fraction it actually is.