Matrix Calculator — Determinant, Inverse & More
Choose 2×2 or 3×3, fill in the matrices, and pick an operation. For 4×4 matrices use the Matrix tab in the full Calvo calculator.
Matrix A
Matrix B
Result will appear here.
How each operation works
- Determinant (2×2): for [[a, b], [c, d]] it is ad − bc. For 3×3, expand along the first row using cofactors.
- Inverse: A¹ exists only when det(A) ≠ 0. It equals the adjugate divided by the determinant. For a 2×2 matrix: (1/det) × [[d, −b], [−c, a]].
- Transpose: swap rows and columns.
- Multiplication: each entry is the dot product of a row of A with a column of B. Order matters: A×B is usually not equal to B×A.
Worked example: for A = [[1, 2], [3, 4]], det = 1×4 − 2×3 = −2, and the inverse is (1/−2) × [[4, −2], [−3, 1]] = [[−2, 1], [1.5, −0.5]].
FAQ
When does a matrix have no inverse?
When its determinant is 0. Such a matrix is called singular.
Can I multiply matrices of different sizes?
In general yes if the columns of A equal the rows of B, but this page uses square matrices of the same size. Use the full Calvo calculator's Matrix tab for more.
Why is A×B different from B×A?
Matrix multiplication is not commutative. The row-by-column rule gives different results when the order changes.
Does it support 4×4?
The full Calvo calculator supports up to 4×4. This page focuses on 2×2 and 3×3.